Question

Prove that `1/2(cotx-tanx)=cot2x`?

Answer 1

Please see below.

Explanation:

`1/2(cotx-tanx)`

= `1/2(cosx/sinx-sinx/cosx)`

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

= `(cos^2x-sin^2x)/(2sinxcosx)`
.
= `(cos2x)/(sin2x)`

= `cot2x`