Question

How do you simplify `csc^2(-x)cos^2x(pi/2-x)`?

Answer 1

Express both factors in terms of `sinx`

Explanation:

`cscx=1/sinx`

`cos(pi/2-x) = sinx`

and `sin(-x) =-sinx`

So:

`csc^2(-x) cos^2(pi/2-x) = 1/sin^2(-x)sin^2(x) =1/(-sinx)^2sin^2(x)=1`

Strictly speaking this is only true for `x!=kpi` where the original expression is not defined.