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

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Answer 1 · 2016-11-28T16:36:48

Express both factors in terms of $sinx$

$cscx=1/sinx$

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

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.

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