Question

How do you simplify the expression `(1-cscx)/(1-csc^2x)`?

Answer 1

`(1-csc(x))/(1-csc^2(x)) = color(green)(1/(1+csc(x)))`

Explanation:

Remember `a^-b^2=(a-b)(a+b)`
So
`color(white)("XXX")1-csc^2(x)=(1-csc(x))(1+csc(x))`
and
`(1-csc(x))/(1-csc^2(x))=cancel(1-csc(x))/(cancel(""(1-csc(x)))(1+csc(x))`