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Identities2 Practice Problems

The document contains a list of practice problems focused on proving various trigonometric identities. Each problem presents a different identity involving functions such as tangent, cotangent, sine, and cosine. The problems range from basic to more complex identities, providing a comprehensive exercise for understanding trigonometric relationships.

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53 views1 page

Identities2 Practice Problems

The document contains a list of practice problems focused on proving various trigonometric identities. Each problem presents a different identity involving functions such as tangent, cotangent, sine, and cosine. The problems range from basic to more complex identities, providing a comprehensive exercise for understanding trigonometric relationships.

Uploaded by

SN
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Lecture Notes Trigonometric Identities 1 page 2

Practice Problems

Prove each of the following identities.

cos x 1 cot x ! 1 1 ! tan x


1. tan x + = 11. =
1 + sin x cos x cot x + 1 1 + tan x

2. tan2 x + 1 = sec2 x 12. (sin x + cos x) (tan x + cot x) = sec x + csc x

1 1 sin3 x + cos3 x
3. ! = 2 tan x sec x 13. = 1 ! sin x cos x
1 ! sin x 1 + sin x sin x + cos x

4. tan x + cot x = sec x csc x cos x + 1 csc x


14. 3 =
sin x 1 ! cos x
1 + tan2 x 1
5. = 1 + sin x 1 ! sin x
2
1 ! tan x cos2 x ! sin2 x 15. ! = 4 tan x sec x
1 ! sin x 1 + sin x

6. tan2 x ! sin2 x = tan2 x sin2 x 16. csc4 x ! cot4 x = csc2 x + cot2 x

1 ! cos x sin x sin2 x 1 ! cos x


7. + = 2 csc x 17. =
sin x 1 ! cos x 2
cos x + 3 cos x + 2 2 + cos x

sec x ! 1 1 ! cos x tan x + tan y


8. = 18. = tan x tan y
sec x + 1 1 + cos x cot x + cot y

9. 1 + cot2 x = csc2 x
1 + tan x cos x + sin x
19. =
csc2 x ! 1 1 ! tan x cos x ! sin x
10. = cos2 x
csc2 x

20. (sin x ! tan x) (cos x ! cot x) = (sin x ! 1) (cos x ! 1)

c copyright Hidegkuti, Powell, 2009


" Last revised: May 8, 2013

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