Question

How do you simplify `(sin(x) * cos (x))/(1-cos^2 (x))`?

Answer 1

`(cosx)/(sinx)`

Explanation:

Given,

`(sinxcosx)/(1-cos^2x)`

Replace `1-cos^2x` with `sin^2x`.

`=(sinxcosx)/(sin^2x)`

Cancel out `sinx` which appears in the numerator and denominator.

`=(sinxcosx)/(sinxsinx)`

`=(color(red)cancelcolor(black)sinxcosx)/(color(red)cancelcolor(black)sinxsinx)`

`=color(green)(|bar(ul(color(white)(a/a)color(black)((cosx)/(sinx))color(white)(a/a)|)))`