Question

Sin^2theta (1-csc^2theta)?

Answer 1

The expression simplifies to `-cos^2theta`

Explanation:

Recall that `csctheta = 1/sintheta`.

`=sin^2theta(1 - 1/sin^2theta)`

`=sin^2theta - sin^2theta/sin^2theta`

`=sin^2theta- 1`

Now recall that since `cos^2x+ sin^2x = 1`, `sin^2x- 1= -cos^2x`.

`=-cos^2theta`

Hopefully this helps!