Answers
Answer:
Hi mate!
To prove:-[tex] \bf \sqrt{ \frac{1 + \sin( \theta)}{1 - \sin( \theta)} } = \sec( \theta) - \tan( \theta) [/tex]
Step-by-step explanation:
By taking LHS,
[tex] \maltese \: \: \large \bf \sqrt{ \frac{1 + \sin( \theta)}{1 - \sin( \theta)} } [/tex]
By rationalisation method,[tex] : \longrightarrow \bf \sqrt{ \frac{1 + \sin( \theta)}{1 - \sin( \theta)} \times \frac{1 + \sin( \theta)}{1 + \sin( \theta)} } \\ \\ : \longrightarrow \frac{ {( \sqrt{1 + \sin\theta }) }^{2} }{( \sqrt{1 - \sin( \theta)})(\sqrt{1 + \sin( \theta)}) } \\ \\ : \longrightarrow \frac{ {( \sqrt{1 + \sin\theta }) }^{2} }{ \sqrt{ {1}^{2} - { \sin}^{2} \theta } } \: \\ \\ : \longrightarrow \: \frac{1 + \sin \theta}{ \cos \theta } \\ \\ \longrightarrow \: \frac{1}{ \cos \theta } + \frac{ \sin \theta}{ \cos \theta} [/tex]
[tex] \: \: \: \: \: \bigg\lgroup \because \: \frac{1}{ \cos \theta }\: = \sec \theta \: \\ \: \: \: \: \: \: \: \: \: \: \: \frac{ \sin \theta}{ \cos \theta} = \tan \theta \bigg \rgroup[/tex]
[tex] \implies \boxed{\pink{ \sec \theta + \tan \theta }}[/tex]
Now taking RHS
[tex] \sf \sec \theta + \tan \theta [/tex]
[tex]\implies \: \: \frac{1}{ \cos \theta } + \frac{ \sin \theta}{ \cos \theta} \\ \\ \implies \frac{1 + \sin \theta }{ \cos \theta } [/tex]
Hence, proved
Answer:
[tex]\large{\pink{\underline\textsf{To Prove :-}}}[/tex]
[tex] \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } = \sec \theta + \tan \theta[/tex]
[tex] \huge{\orange{\underline{\textsf{Solution :-}}}}[/tex]
[tex] \sf \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } [/tex]
First we have to rationalize it to remove the square rootNow we will multiply √1+sinθ both sides[tex] \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } \times \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } \\ \sqrt{ \frac{ {(1 + \sin \theta) }^{2} }{(1 + \sin \theta)(1 - \sin \theta) } } \\ \sqrt{ \frac{ {(1 + \sin \theta) }^{2} }{1 - { { \sin}^{2} \theta } } }[/tex]
We know that sin²θ + cos²θ = 1so cos²θ = 1 - sin²θ[tex] \sqrt{ \frac{( {1 + \sin \theta })^{2} }{ { \cos}^{2} \theta} } \\ \frac{1 + \sin \theta }{ \cos \theta } \\ \frac{1}{ \cos \theta} + \frac{ \sin \theta }{ \cos \theta } [/tex]
[tex]\sf{\red { \sec \theta + \tan \theta}}[/tex]
[tex] \sf \huge \purple {HENCE \: \: PROVED! }[/tex]
Related Questions
100 Points!!! WILL MARK BRAINLIEST!!!
Daisy is a botanist who works for a garden that many tourists visit. The function f(s) = 3s + 35 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 15w represents the number of seeds she plants per week, where w represents the number of weeks.
Part A: Write a composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks. (4 points)
Part B: What are the units of measurement for the composite function in Part A? (2 points)
Part C: Evaluate the composite function in Part A for 36 weeks. (4 points)
Answers
Answer:
A) [tex]f(w)=45w+35[/tex]
B) f(w) is the total number of flowers that bloomed
w is the number of weeks
C) 1655 flowers
Step-by-step explanation:
Part A
[tex]f(s) = 3s + 35[/tex]
[tex]s(w) = 15w[/tex]
To create the composite function, replace the variable [tex]s[/tex] in the function f(s) with function s(w):
[tex]\implies f(w)=3(15w)+35[/tex]
[tex]\implies f(w)=45w+35[/tex]
Part B
f(w) is the total number of flowers that bloomedw is the number of weeksPart C
Substitute w = 36 into the compositie function and solve:
[tex]\implies f(36)=45(36)+35=1655[/tex]
What is the value of the expression below if C = 5 and d = 7? A. 65 B.315 c. 15 d. -7
Answers
Answer:
Step-by-step explanation:
=2(5)^2 - 5(7)
= 2(25) - 35
= 50 - 35
= 15
What is the value of χ2 for the two-way table?
A B C D
X 5 10 15 20
Y 7 13 17 21
(2 points)
0.5320
0.0801
1.08
0.2830
0.9632
Answers
Answer:
0.2830
Step-by-step explanation:
Observed Values
Add totals for the rows and columns to the two-way table (see attachment 1).
Expected Values
Create an "Expected Values" table by multiplying each row total by each column total and dividing by the overall total (see attachment 2).
Chi-square test statistic
[tex]\sf \dfrac{(observed-expected)^2}{expected}[/tex]
Create a third table by using the formula to calculate the chi-square test statistic for each cell of the table (see attachments 3 and 4)
Chi-square
Add the values from the table in attachment 4.
[tex]\sf X^2=0.05556+0.03945+0.002315+0.05465+0.04789+0.03401+0.001996+0.04711[/tex] [tex]\implies \sf X^2=0.2830 \:(4 \:sf)[/tex]
PLS HELP!!!! No links pls and Ty<3333
Answers
Answer:
The Circumference is 150.7 inches
Step-by-step explanation:
The cricumference of a circle is given by the formula:
[tex]C = 2\pi r[/tex]
We are given the radius and are given 3.14 for pi.
Substituting these values into the euation gives us:
C = 2(3.14)(24)
C = (6.28)×(24) = 150.72
The Circumference is 150.7 inches to the nearest tenth.
Algebra II | Progressions
It’d be very much appreciated if someone could a.) solve this for me, and b.) kindfully explain how to get the correct answer in simple terms. It looks easy, but the lesson isn’t making it make sense. Thank you! :)
Answers
Answer:
Option 1
Step-by-step explanation:
Substiute the value of n with 1 to 6 and find each term.
When n = 1 ,
[tex]\sf First \ term = \dfrac{1}{2*1+1}=\dfrac{1}{2+1}=\dfrac{1}{3}\\\\[/tex]
[tex]\sf When n = 2,\\\\Second \ term = \dfrac{2}{2*2+1}=\dfrac{2}{4+1}=\dfrac{2}{5}\\\\[/tex]
When n = 3 ,
[tex]\sf Third \ term = \dfrac{3}{2*3+1}=\dfrac{3}{6+1}=\dfrac{3}{7}[/tex]
When n = 4,
[tex]\sf Fourth \ term =\dfrac{4}{2*4+1}=\dfrac{4}{8+1}=\dfrac{4}{9}\\[/tex]
When n = 5 ,
[tex]\sf Fifth \ term = \dfrac{5}{2*5+1}=\dfrac{5}{10+1}=\dfrac{5}{11}\\\\When \ n = 6,\\\\ \: Sixth \ term =\dfrac{6}{6*2+1}=\dfrac{6}{12+1}=\dfrac{6}{13}[/tex]
[tex]Answer: \dfrac{1}{3}+\dfrac{2}{5}+\dfrac{3}{7}+\dfrac{4}{9}+\dfrac{5}{11}+\dfrac{6}{13}[/tex]
help me please please
Answers
Answer:
5 units down, two to the left. Therefore, x+-2, y+-5
Step-by-step explanation:
Suzie paid a total of \$324$324dollar sign, 324 for xxx tickets to a rock festival.
How much did each ticket cost?
Write your answer as an expression
Answers
Answer:
324/x
khan let me know
The function H(n) describes the total amount of money a movie theater receives for n ticket sold.
which domain is appropriate for this function.
all integers
all real numbers
all positive integers and zero
or
all positive real numbers and zero
Answers
The domain which is appropriate for the function, H(n) is; all positive integers and zero.
Domain of functionsFrom the task content;
We are required to identify the domain which is most appropriate for the function.On this note, we are required to determine the possible values for the number of tickets bought, n.
Ultimately, since tickets are whole, it follows that the appropriate domain for this function is; all positive integers and zero.
Read more on domain of functions;
https://brainly.com/question/1369616
can anyone solve this?
Answers
Answer:
The answer is 14/50
Step-by-step explanation:
sin=opp/hyp
sin=14/50
A market research company wants to collect opinions on the comfort and performance of a new type of sneaker by brand x. which group of individuals would be the best choice for a random sample? ask every fourth person on the street ask every fourth person who is wearing that brand of sneaker ask every fourth employee from the brand x flagship store ask every fourth person who is wearing shoes
Answers
The group of individuals would be the best choice for a random sample is to ask every fourth person who is wearing that brand of sneaker.
We have,
A market research company wants to collect opinions on the comfort and performance of a new type of sneaker by brand x.
We have to determine which group of individuals would be the best choice for a random sample.
What is the simple random sampling?
A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen
One of the best methods in random sampling is called quartering.
In quartering, the population is divided into 4 quadrants and the
the sample is obtained on one of the quadrants obtained.
In this case, the procedure to do is:
To ask every fourth person who is wearing that brand of sneaker.
Therefore option A is correct.
To learn more about the sampling visit:
https://brainly.com/question/12892403
Answer:
It's b
Step-by-step explanation:
Took it on edge 2022
100 Points!! 0_0
Solve and check for extraneous solutions.
5(3x+1)^1/2=10
Please SHow Steps!!! WIll give the brainiest!!
Answers
[tex]5\sqrt{3x+1} = 10\\\\\implies \sqrt{3x+1} = \dfrac{10}5 \\\\\implies \sqrt{3x+1} = 2 \\\\\implies 3x +1 = 4\\\\\implies 3x = 4-1 \\\\\implies 3x = 3\\\\\implies x =1[/tex]
Answer:
x = 1
Step-by-step explanation:
Given equation:
[tex]\dfrac{5(3x+1)^1}{2} =10[/tex]
If a term has "1" as it's exponent, it means that it's the number itself. Therefore, we can remove the "exponent".
[tex]:\implies\dfrac{5(3x+1)}{2} =10[/tex]
Simplify the distributive property:
[tex]:\implies\dfrac{15x+5}{2} =10[/tex]
Using cross multiplication:
[tex]:\implies15x+5} =10 \times 2[/tex]
Simplify the R.H.S:
[tex]:\implies15x+5} =20[/tex]
Subtract 5 both sides:
[tex]:\implies15x+5 - 5} =20 - 5[/tex]
Simplify both sides:
[tex]:\implies15x} =15[/tex]
Divide 15 both sides:
[tex]:\implies\dfrac{15x}{15} } =\dfrac{15}{15}[/tex]
Simplify both sides:
[tex]:\implies x= 1[/tex]
The circumference of a circular field is 166.42 yards. What is the diameter of the field? Use 3.14 for it and do not round your answer.
Answers
2×3.14×r = 166.42
3.28r = 166.42
r = 166.42/3.28
r = 50.7378049
diameter = 2×radius
diameter = 2 × 50.7378049
diameter = 101.47561
Answer:
52.98
Step-by-step explanation:
See attached image to find radius
diamater = Radius * 2
26.49 Yards * 2 = 52.98
A right cylinder with a diameter of 8 ft and a height of 15 ft. Help!!
Answers
Given :-
Diameter = 8ft , radius = 4ft.Height = 15ftWe can find Total Surface Area , Lateral Surface Area and Volume of Cylinder by given values.
Volume of Cylinder = πr²h
putting the known values ,Volume = 3.14×4²×15 cubic feet
Volume = 753.6 cubic feet
Total Surface Area of Cylinder = 2πr(r+h)
TSA = 2×3.14×4(4+15) square feet
TSA = 477.28 square feet
Lateral Surface Area Of Cylinder = 2πrh
CSA = 2×3.14×4×15
CSA = 376.8 square feet
please teach me how to do this
Answers
Answer:
16.4
Step-by-step explanation:
x = radius
x = 8.7 + 7.7
x = 16.4
Which set of three side lengths will not from a triangle
A 17, 12, 6 C 36, 14, 27
B 25, 38, 13 D 39, 44, 6
Answers
Answer:
5tv. 9. v. 9. 9. o. o. o o. o. 9.
What is the value of the expression 16 + 56/n when n = 8?
Answers
Answer:
23
Step-by-step explanation:
[tex]16 + \frac{56}{n} [/tex]
[tex]where \: n = 8[/tex]
[tex]16 + \frac{56}{8} [/tex]
[tex]23[/tex]
[tex]56 / 8 = 7[/tex]
Add second[tex]7 + 16 = 23[/tex]
With that information, your answer is twenty-three.
5 x ( 3 + h ) = 15 + 45
Answers
Answer:
h=9
Step-by-step explanation:
I did this one and it was right for pre- algebra,
equation of circle: mastery test HELPPPP PLS !!
Answers
PQ is the diameter so the midpoint of PQ is the center of the circle. if we suppose the center point of the circle called o then ;
[tex]o = \frac{pq}{2} \\ [/tex]
[tex]pq = \sqrt{ { (- 10 - 6})^{2} + ({10 - ( - 2)})^{2} } [/tex]
[tex]o = \frac{( -10 ,10) + (6 , - 2) }{2} \\ [/tex]
[tex]o = \frac{( - 10 +6 ,10 - 2)}{2} \\ [/tex]
[tex]o = ( \frac{ - 4}{2} , \frac{8}{2} ) \\ [/tex]
[tex]o = ( - 2,4)[/tex]
For the second step we need to find the radius of the circle which has the half the PQ distance measure, so we have to find the the PQ distance and divide it by 2 :
_____________________________________________
As u know the distance between 2 point is going to find by following formula :
[tex]pq = \sqrt{ {(x(p) - x(q)})^{2} + {(y(p) - y(q)})^{2} } \\ [/tex]
[tex]pq = \sqrt{ ({ - 10 - 6})^{2} + ({10 - ( - 2)})^{2} } [/tex]
[tex]pq = \sqrt{ ({ - 16})^{2} + ({12})^{2} } [/tex]
[tex]pq = \sqrt{256 + 144} [/tex]
[tex]pq = \sqrt{400} [/tex]
[tex]pq = 20[/tex]
Thus :
[tex]radius = \frac{pq}{2} \\ [/tex]
[tex]radius = \frac{20}{2} \\ [/tex]
[tex]radius = 10[/tex]
_____________________________________________
Ok we're almost done cuz we have what we needed:
If we suppose that the first coordinate of the center is a and the second coordinate of the center is b and the radius shown by r then :
[tex] ({x -a})^{2} + ( {y - b})^{2} = {r}^{2} [/tex]
Is the equation of the circle in the standar form thus :
[tex] ({x - ( - 2)})^{2} + ({y - 4})^{2} = {10}^{2} \\ [/tex]
[tex] ({x + 2})^{2} + ({y - 4})^{2} = 100[/tex]
As u can see option B is the correct answer.
And we're done ...
Have a great day ♡♡♡♡♡find the absolute value of -5/8
Answers
Answer:
5/8
Step-by-step explanation:
To find the absolute value you simply remove the negative symbol
All the dimensions of a pentagon were multiplied by the same factor, and the area of the figure changed by a factor of 25. By what factor were the dimensions of the pentagon multiplied?
12. 5
625
5
50
Answers
Answer:
625
Step-by-step explanation:
I just did this question
Solve the following equation using distribution. 1 2 (4x − 12) = 5 ( 1 2 ) (4x) − ( 1 2 ) (12) = 5 2x − 6 = 5 +6 +6 2x = 11 What is the value of x? 5.5 9 11.5 13
Answers
Answer:
5.5
Step-by-step explanation:
Answer: IT IS 5.5I DID THE TEST
Step-by-step explanation:
Can someone pleas help???????
Answers
Answer:
written all the angles below:
m<1 = 35°
m<2 = 77°
m<3 = 49°
m<4 = 77°
m <5 = 62°
m<6 = 28°
hope that helps...
everday at 9:15 am jessie takes his for a walk for 30 min he takes the next 2 hours to work on his computer before he eats lunch what time does he eat lunch
Answers
Answer:
11:45 AM
Step-by-step explanation:
9:15 +30 mins is 9:45
9:45 +2 hours is 11:45
Hope this helps!
HELP NOW! RIGHT ANSWER=BRAINLIEST
EXCUSE NAIL POLISH!!!!
Answers
Answer:
60
Step-by-step explanation:
6% of 250 = 15 = 250 * 0.06
30% of 250 = 75 = 250 * 0.7
75-15=60
Answer:
60
Step-by-step explanation:
Lane loads his stuck with 3 tons of bricks. How many pounds of bricks does he have
Answers
2000 pounds in a ton
Find the area of the figure
Answers
Step-by-step explanation:
there is one central rectangle :
from (-4, 2) to (2, -2).
that means it dimensions are 6×4 (for x from -4 to +3, for y from +2 to -2).
and then there are 3 additional triangles
(2, -4) (2, 2) (6, 2)
(-4, -2) (2, -2) (2, -4)
(-6, 2) (-4, 2) (-4, -2)
with the leg lengths
(2, -4) to (2, 2) = 6, and (2, 2) to (6, 2) = 4
(-4, -2) to (2, -2) = 6, and (2, -2) to 2, -4) = 2
(-6, 2) to (-4, 2) = 2, and (-4, 2) to (-4, -2) = 4
the area of the rectangle is
6×4 = 24 square units
the area of the first triangle is
6×4/2 = 3×4 = 12 square units
the area of the second triangle is
6×2/2 = 6 square units
the area of the third triangle is
2×4 = 8 square units.
so, the total area is
24 + 12 + 6 + 8 = 50 square units.
What are three ratios that are equivalent to 16:12.
Answers
Answer:
4:3 = 8:6 = 12:9 = 16:12 = 20:15 = 24:18 = 28:21 = 32:24 = 36:27 = 40:30
Step-by-step explanation:
Answer:
8:4, 32:24, 48:36
Step-by-step explanation:
16 ÷3=8
12÷3=4
↓
8:4
----------------------
16 ×2=32
12×2=24
↓
32:24
-----------------------
16×3=48
12×3=36
↓
48:36
Hope this helps! Have a good day! : )
Dividing by 1/2 means you are finding how many halves are in the dividend
Answers
to multiply it by 2 because two is the dividend and that is closest to 1
What is the exact circumference of a circle with a radius of 17 mm?
•
8.5T mm
O
177 mm
O 347 mm
O
687 mm
Answers
Answer:
[tex]34\pi[/tex]
Step-by-step explanation:
Given,
r = 17 mm
→ Circumference =
[tex]2\pi \: r[/tex]
→ 2x3.14x17
→ 34x3.14 =
[tex]34\pi[/tex]
↓
c = 106.76 mm
4-5 practice proving right triangles congruent worksheet 1-7
Answers
Step-by-step explanation:
1. mzoGE = M2GOE
1. Given
2. GE = OE
2.
3. E is the midpoint of AT
3. Given
4. AE ET
4. Definition of the midpoint of a line segment.
5. AE = ET
5. Congruent segments have equal length.
6. MLAEG > MZTEO
6. Given
7. AG > TO