Question

Simplify `sinx/cot^2x-sinx/cos^2x`?

Answer 1

`sinx/cot^2x-sinx/cos^2x=-sinx`

Explanation:

`sinx/cot^2x-sinx/cos^2x`

= `sinxtan^2x-sinxsec^2x`

= `sinx(tan^2x-sec^2x)`

= `sinx(tan^2x-(tan^2x+1))`

= `sinx(tan^2x-tan^2x-1)`

= `sinx xx-1`

= `-sinx`