Algebraic*Trig*Worksheet**1) Simplify*the*Following:*

a) 1− csc x − cos x ⋅cot x( )2cos x

*

**

***

b) *−

csc xsin x

−1

cot x ⋅sin xcos2 x −1

*** *

**

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c) 3− 3csc2 x

− 2sec2 x

1+ cos1+ sec

⎛⎝⎜

⎞⎠⎟2 **

******

d) −cot2 x − 1tan2 x

⎛⎝⎜

⎞⎠⎟

1csc x

− tan xcos x

csc x − csc x ⋅ 1sec2 x

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟**

******

e) cos x sin3 x + sin3 xcos x ⋅sin x

+

2tan x

⋅ csc xsec x

cot xsin x

+ sin x ⋅cos x ⋅sec2 x

1− cos2 x

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟**

** *

2) sin 18!( ) = 5 −1

4.*Find* sin 78! .**

Hint:* sin(A + B) = sinAcosB + cosAsinB **

*******3) Evaluate* cos arcsin 3

5 − arctan 512( ) .*

*Hint:* cos(A − B) = cosAcosB + sinAsinB ********

*4) Evaluate* tan arcsin x + arctan y( ) .**

Hint:* tan(A + B) = tanA + tanB1− tanA tanB

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5) Earlier*in*the*term,*there*was*a*HW*question*that*was*impossible*without*the*double*angle*formula.*I*told*you*to*just*assume*that* sin 2x( ) = 2sin xcos x .*Prove*this*fact*using*an*angle*addition*formula.**

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