Trigonometric Identities Worksheet

[Pages:3]I. Prove each identity

1) tanxcos x =sinx

3) sin x cot x == cos x 5) S' lnxt=an-x

secx

Trigonometric Identities Worksheet

2) cotxsec x = esc x

4) tan xcsc x == sec x

6) -c-o=tx=

cosx

cscx

II. Prove each identity 1) esc x(l + sin x) == 1 + esc x 3) coscx(secx-1)=1-cosx

5) 1- tan x = -tanx

1- cotx

2) sinx(l+cscx)=l+sinx 4) sinxsecxcotx == 1

6) cot x =1 +-co-t x

1 + tan x

III. Prove each identity

1)

sm. x tan x

+ sec x

sin2 x + 1

== - - -

cosx

3) 1+ sin x esc x + 1

1- sin x esc x-I

5) -l+-s-i= nx sm. x 1+ cscx

2) 1 + cos x 1 + sec x

1- cos x sec x-I

6) -si-n-x-+ -ta=n xt

a n x cos x + 1

Mathematics 536

Trigonometric Identities

Sheet I

Verify each of the following:

1. sec S - sec Ssin l S = cos S 2. sinSsecScotS =1

4. sin l Ssec l S - sec l S = -1

5. (sinx+cosx/ +(sinx-cosx/ = 2

7. tanx+ cos x = secx

1+sinx 8. sinxsecx=tanx

9. (1 -sin l t)(1 +tan l t) = 1 10. (1- cos A)(1 + sec A)cot A = sin A

11. csc l 8(1- cos l 8) =1

12. sinS + cosS = 1

cscS sec S

1-2cosl X

13.

=tanx-cotx

sinxcos x

15. sinAcosA(tanA+cotA) =1

16. 1- cos l x = sinx

1+ sinx

17.

1

= sec x - tan x

sec x +tanx

18. 2 cscx= sinx +1+-c-osx

1+ cos x sin x

...... ~. .

302 PROPERTIES OF TRIGONOMETRIC FUNCTIONS

9.

+ sin u + 1 -

== 2 sec 2u

SIn U

1 + sec u

10.

sec U

sin 2u - cos u

1 - cos U

sin u

II.

Sin U - 1+ cos U

12.

sec u - 1 sec u + 1

1 - cos u

1 + cos u

13. - - - - - SIn U sec u - tan u

14.

cos

u

cot

u

==

-

.1 - -

.

SIn

U

SIn U

15.

tan

A

+

-1-

==

sec A

-~

tan A sin A

16.

sin A + tan A 1 + sec A

==

sin

A

1

tan 2A

17. 1+-~==---

cos A sec A -

18. sin x + cos x == -+-t-an x

sec x

19. tan u == -1 +-s-in -u --c-os-2 u cos u (1 + sin u)

20. cot u == 2 + csc u - 2 cos u

sec u

21.

tan A sin A

tan A - sin A -------

tan A + sin A tan A sin A

22. -se-e4 u-+- -tan=4 u=e-os-4 u+ 2

sec2 u tan 2 u sin 2 u

23. --c- ot-A - + - esc-A-

~ _ -sec A 24. cot 2A sec2A == 1 + cotZA

sin A - cot A - csc A

25.

cot tan

A A

+ +

cot tan

B B

+

1I-

cot A cot B == 0

tan A tan B

26. sin A cos A _ - -sin-2 A-

1 - cos A tan A - sin A

27. sin u sec u cot u == 1

.

v

29.

-+c-oss-iun-u

+

-+- s-in-u

==

cos u

2

sec

u

32.

-sin-4 u-- -c-os4-u == sin 4 u

1 - eot4 u

33. 1 - 2 sin u - 3 sin 2U 1 - 3 sin u

cos 2 u

- 1 - sin u

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

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download