Question

How do you prove that `-cot2x = (sec^2x-2)/(2tanx`?

Answer 1

Please refer to a Proof in the Explanation.

Explanation:

Knowing that, `tan2x=(2tanx)/(1-tan^2x)`, we have,

`-cot2x=-1/(tan2x)=(tan^2x-1)/(2tanx)={(sec^2x-1)-1}/(2tanx)`.

`rArr -cot2x=(sec^2x-2)/(2tanx)`.