Question

1.) cot(-θ)(secθ)
I think the answer is secθ but I don't know how to get this.

2.) (tanθ) / (cos)(90° -θ)

3.) 3sin2xcos2x - sin4x

4.) (cosx + tanx) / (csc^2 x)

Answer 1

cot(-θ)(secθ)
= cos(-Ø)/sin(-Ø)(1/cosØ
= (cosØ/-sinØ)(1/cosØ
= - 1/sinØ
= - csc(Ø)

(test your answers with some weird angle, don't use 30's , 60's, or 45's)

2. you will have to know that
cos(90°-x) = sinx
take it from there

3. 3sin2xcos2x - sin4x
= 3sin2xcos2x - 2sin2xcos2x
= sin2xcos2x
or (1/2)sin4x

4. change everything to sines and cosines and just mess around with it.

make sure to test your answer vs the original with some strange angle on your calculator.