Prove the Identity:
[tex] \large{ \frac{cos( - \theta)}{1 - sin \theta} - \frac{cos( \theta + \pi)}{1 + sin \theta} = \frac{2}{cos \theta} }[/tex]
Show your work, thanks! ​

Answers

Answer 1

Answer:

Use properties:

cos(-θ) = cosθcos(θ + π) = - cosθsin²θ + cos²θ = 1

Solution:

cosθ/(1 - sinθ) - (-cosθ)/(1 + sinθ) = cosθ([1/(a- sinθ) + 1/(1 + sinθ)] = cosθ[(1 + sinθ + 1 - sinθ)/(1 - sin²θ)] = cosθ(2/cos²θ) = 2/cosθ

Proved

Answer 2

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

[tex]\sf{\dfrac{cos( - \theta)}{1 - sin \theta} - \dfrac{cos( \theta + \pi)}{1 + sin \theta} }[/tex]

[tex]\\[/tex]

[[tex]\tt{cos(-\theta)=cos\theta }[/tex] ]

[tex]\sf{\dfrac{cos \theta}{1 - sin \theta} - \dfrac{cos( \theta + \pi)}{1 + sin \theta}}[/tex]

[tex]\\[/tex]

[[tex]\tt{cos(\theta+\pi)=-cos\theta }[/tex] ]

[tex]\sf{\dfrac{cos \theta}{1 - sin \theta} - \dfrac{-cos\theta }{1 + sin \theta}}[/tex]

[tex]\sf{\dfrac{cos \theta}{1 - sin \theta} + \dfrac{cos\theta }{1 + sin \theta}}[/tex]

[tex]\\[/tex]

[tex]\sf{cos\theta(\dfrac{1}{1-sin\theta}+\dfrac{1}{1+sin\theta} ) }[/tex]

[tex]\sf{cos\theta(\dfrac{1+sin\theta+1-sin\theta}{(1)^2-(sin\theta)^2 })}[/tex]

[tex]\sf{cos\theta(\dfrac{1\cancel{+sin\theta}+1\cancel{-sin\theta}}{(1)^2-(sin\theta)^2 })}[/tex]

[tex]\sf{cos\theta(\dfrac{2}{1-sin^2\theta })}[/tex]

[tex]\\[/tex]

[[tex]\tt{1-sin^2\theta=cos^2\theta }[/tex] ]

[tex]\sf{cos\theta(\dfrac{2}{cos^2\theta })}[/tex]

[tex]\sf{cos\theta(\dfrac{2}{cos\theta×cos\theta })}[/tex]

[tex]\sf{\cancel{cos\theta}×(\dfrac{2}{cos\theta×\cancel{cos\theta} })}[/tex]

[tex]\sf{\dfrac{2}{cos\theta} }[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex] \therefore{ \frac{cos( - \theta)}{1 - sin \theta} - \frac{cos( \theta + \pi)}{1 + sin \theta} = \frac{2}{cos \theta} }[/tex](proved)


Related Questions

An ice cream shop offers 6 different flavors of ice cream and 11
different toppings. How many choices are possible for a single
serving of ice cream with one topping?

Answers

Answer:

66

Step-by-step explanation:

Since these two events are independent, multiply the two probabilities together:

6*11 = 66 (choices)

Written as a simplified polynomial in standard form, what is the result when (3x+7)^2 is subtracted from 3?

Answers

Given:

[tex](3x+7)^2[/tex] is subtracted from 3.

To find:

The result of the given statement in the standard form of the polynomial.

Solution:

We need to find the result when [tex](3x+7)^2[/tex] is subtracted from 3.

So, the resulted polynomial can be written as:

[tex]P(x)=3-(3x+7)^2[/tex]

On simplification, we get

[tex]P(x)=3-((3x)^2+2(3x)(7)+(7)^2)[/tex]               [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]

[tex]P(x)=3-(9x^2+42x+49)[/tex]

[tex]P(x)=3-9x^2-42x-49[/tex]

[tex]P(x)=-9x^2-42x-46[/tex]

Therefore, the resulted polynomial in standard form is [tex]-9x^2-42x-46[/tex].

How do I solve these problems?

Answers

6) 18,26,34
Add 8 each time
… 42,50,58,66,74,82,90,98,106,114,122,130
The 15th term in the sequence would be 130

HELP ME PLEASE PLEASE PLEASE PLEASEEEEEEEEEEEEE
Use the function f(x) to answer the questions:

f(x) = 2x2 − 5x + 3

Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)

Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)

Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

Answers

Answer:

part A: x= 1 and x= 3/2

part B: minimum at (5/4, f(5/4))

Step-by-step explanation:

part A: factoring

0 = 2x^2 - 5x + 3

= (2x^2 - 2x)(-3x + 3)

= 2x(x - 1) -3(x-1)

= (2x - 3)(x - 1)

x= 1 and x= 3/2

part B: candidates test

find the derivative of the function.

f(x) = 2x^2 - 5x + 3

f'(x) = 4x -5

solve for critical numbers.

0 = 4x - 5

x = 5/4

candidates test by plugging in numbers into the derivative to see if that area is negative or pos.

f has a minimum at x = 5/4 because f' goes from neg to pos there. to find the coordinate for x = 5/4 just plug it into the original function to find f(5/4).

Part C: to draw the graph, I'd just plot the vertex coordinate that you solved for in part B, then I would plot the x intercepts that you solved for in part a, from there just draw a line throu the 3 points. (it should look like a U shape)

Washington Middle School has a supply store for students. The graph shows the total sales of the supply store for each month over the school year.
525
450
375
Total Sales (dollars)
300-
225
150
75+
0
10
Month
What is the rate of change in total sales from month 8 to month 9?
O A. -100 dollars per month
OB. -75 dollars per month
C.-50 dollars per month
оо
OD. -25 dollars per month

Answers

Answer:

B??

Step-by-step explanation:

It is a little hard to understand because of hot it looks, BUT 300-225 is 75, 225-150=75, 150-75=75,75-70=75

Find the missing angle...

Answers

Answer:

15 degrees

Step-by-step explanation:

Because you add 115 and 50 to get 165. And we know that a triangles angles when added up will equal 180. So you subtract 180 and 165 to get 15 degrees, your missing angle!

Hope this helps!

Please help me!!!!!!!!!!!!

Answers

Answer:

16.03

Step-by-step explanation:

Which of the following is the equation of a parabola with the focus at (0, 3/4) and the directrix y = -3/4?​

Answers

Answer:

do you have the picture I actually understand it if I see it in pictures .

1 Pound = 16 ounces
2 Pounds 6 Ounces = blank ounces

Answers

[tex]\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}[/tex]

38 ounces.

Thanks.Hope it helps.

Answer:

32 ounces........

..

Step-by-step explanation:

.................

What is 52% of 475?

Help please

Answers

Answer:

247

Step-by-step explanation:

0.52x475=247

i hope this helps :)

Answer:

The answer is 247 because 52% of 475 is 247

Which is the value of (3+1)-(3-1)?
A. -1
o
B. 0
C. 2
C
D. 2i
O E 6+21

Answers

(3+1-(3-1)? Is equivalent to two
The answer is C

(3+1) equals 4
(3-1) equals 2
4-2=2

The ratio of two siblings current age is 1/2. In ten years the ratio of their ages will be 3/4. How old are they now?

Answers

Answer: 3:5

Step-by-step explanation: heres the answer

Which of the following topics is the Broadest?
Kyrie Irving's trade request
The movement of free-agent players
The NBA draft

Answers

Answer:

Step-by-step explanation:

its nba and kyrie

Answer:

nba aND KYRIE

Step-by-step explanation:

Please help with very easy math teach me to understand and I'll give brainliest

Answers

You would use the Pythagorean theorem A squared plus B squared equals C squared so you would for example do 5 squared plus 6 squared equals 8 squared so then in your calculator you would put five squared +6 squared see what that equals then do another thing and put eight squared and if it equal each other than it can make a right angle

Answer:

B

Step-by-step explanation:

since a²+b²=c²

this is proven correct in answer B

As;

(8^0.5)² +(3)²=(17^0.5)²

Helppppppppp! Pleeeeeeeeeaaaaaaaase!

Answers

Answer: (7) I think

Step-by-step explanation:

the way you speak, or your ___, Can let others know how you are feeling


A.tone
B.emotion
C.voice
D.language

Answers

Answer:

A, tone

Tone can also be used in poetry or writing to set the mood. It's kinda like your attitude, so this is the best answer.

Step-by-step explanation:

Answer:

Tone

Step-by-step explanation:

Tone matters more than word choice.

Find the slope of the line that passes through (1, 10) and (9, 9).

Answers

Answer:

Step-by-step explanation:

Use the slope formula=

y2-y1 / x2-x1

the answer is

(-1,8)

Find the area of the following triangle: 17 9 14 10 Note: Figure not to scale.​

Answers

Answer:

I believe 76.5 is the area to the triangle above.

Answer:

76.5

Step-by-step explanation:

the area is half the base× tge height so 1/2 (17)×9

Help ejejsisjensisne ndjzjene Enid we ejsisbenejeusbw

Answers

Answer:

its C bro

its have to be 1-sin2x

because (sinx-cosx)² equal sin²x+cos²x-2×sinx×cosx

C bro the answer is c

Please help! I will give Brainliest!

Answers

Answer:

a. 5/12

Step-by-step explanation:

there are 5 vowels out of 12 letters

can someone explain and show the work for me, i’m so confused on it!

Answers

Answer:

26π

Step-by-step explanation:

The equation for circumference is

c = 2πr

using r = 13

c = 2π(13)

Rearrange

c = 2(13)π

Simplify

c = 26π

Answer:

the answer is 26tt

good luck

the solution to the equation x+5= -9 is​

Answers

Answer:

x = -14

Step-by-step explanation:

-9 -5 = -14

The length of the arc of semi circle is 15 cm calculate the area of the semi circle ?

Answers

Answer:

The area of the semi-circle is 35.8 cm².

Step-by-step explanation:

The length of the arc is given by:

[tex] s = r\theta [/tex]   (1)

Where:

s: is the length of the arc of semi-circle = 15 cm

r: is the radius

θ: is the angle in radians    

Since we need to calculate the area of the semi-circle, the angle is:

[tex] \theta = \frac{360}{2} = 180 = \pi [/tex]  

From equation (1) we can find the radius:

[tex] r = \frac{s}{\theta} = \frac{15}{\pi} [/tex]    

Now, the area of the semi-circle is:              

[tex] A = \frac{\pi r^{2}}{2} = \frac{\pi (\frac{15}{\pi})^{2}}{2} = 35.8 cm^{2} [/tex]

Therefore, the area of the semi-circle is 35.8 cm².

I hope it helps you!                          

What is 2^4 in standard form?

Answers

Answer:

2^4=16

Step-by-step explanation:

2^4 is equal to 2x2x2x2 which is equal to 4x2x2 which is equal to 8x2 which is equal to 16. Therefore, 2^4 is equal to 16.

If this has helped you please mark as brainliest

3
What is the quotient of -3/8 and -1/3

Answers

Answer:

the answer is -1 1/8

Step-by-step explanation:

-3/8 ÷-1/3

= -3/8×3/-1

= -3 × 3

  8 × -1

= 9/8

= -1 1/8

A polling organization announces that the proportion of American voters who favor congressional term limits is 64 percent, with 95% confidence and margin of error of 3 percent. This means that

Answers

Answer:

We are 95% confident that the proportion of American voters who favor congressional term limits is 64 percent with a difference of 3% for small sample size.

Step-by-step explanation:

95 % confidence means that we are 95 % confident that the the proportion of American voters who favor congressional term limits is 64 percent.

95 % confidence  means that of all the sample about 95 %  values are within in the given range.

And only 5% sample are not included in the given parameter.

Margin of error is the amount of miscalculation or difference in change of circumstances from the obtained data.

3% margin of error usually occurs when the data size is small.

As the data size increases the margin of error decreases.

So this statement tells us that we are 95% confident that the proportion of American voters who favor congressional term limits is 64 percent with a difference of 3% for small sample size.

Margin of error= z *σ/√n→

This indicates that as the sample size decreases the margin of error increases and vice versa.

Consider the function f (x) = StartLayout Enlarged left-brace first row negative StartFraction 4 x Over x minus 3 EndFraction, x less-than 5 second row negative 7 x + 25, x greater-than 5 EndLayout. Which type of discontinuity occurs at x = 5? mixed infinite endpoint removable

Answers

Answer:

Its removable

Step-by-step explanation:

yes

this is a removable discontinuity

Here we have the piecewise function:

[tex]f(x) = \frac{-4x}{x - 3}[/tex]     if x < 5

[tex]f(x) = -7x + 25[/tex]    if x > 5.

We want to see which type of discontinuity we have at x = 5.

Remember that:

If we have two asymptotes, then is an infinite discontinuity

if just one point is missing, then it is a removable discontinuity

If the value drastically changes after the discontinuity, then its a jump discontinuity

Mixed case is when two of these happen.

Because we have a piecewise function, we need to evaluate both parts in x = 5.

If both parts give the same value, then we will have a removable discontinuity

if the values are different, then we have a jump discontinuity.

first part:

f(5) = -4×5/(5 - 3) = -20/2 = -10

second part:

f(5) = -7×5  + 25 = -35 + 25 = -10

So we got the same value, which means that this is a removable discontinuity

in the image below you can see the graph of the piecewise function, and see that as x tends to 5, both sides of the function tend to the same value.

if you want to read more about this,, you can see:

https://brainly.com/question/17317969

Please help me pick the right answer

Answers

....................................................................

Answer:

its C

Step-by-step explanation:

5x+2+4x-3=9x-1

hopefully its helpful

What ideas do you have about what makes Anchorage, Alaska, cooler than Christchurch, New Zealand?
+Science

Answers

Answer:

You can explore a variety of things in Alaska. There are so many activities you could do such as visiting museums and hiking and tons more. The thing about this is that it is out in the wilderness which makes it more exciting and cooler to see nature more than it does in new zealand. The climate can be pretty chilly in Alaska but it is way much fun to see tons of glaciers. New zealand has eathquakes frequently whilst Alaska doesn't.

1
What is the value of 3 divided by
2​

Answers

Answer:

1.5

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

its pretty simple- 1 + 1 = 2 .5 + .5 = 1 2 + 1 = 3

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