Question

How do you verify `2cot 2x = cot x - tan x`?

Answer 1

We have that

#cotx-tanx=cosx/sinx-sinx/cosx=(cos^2x-sin^2x)/(sin*cosx)= 2*(cos2x)/(2sinxcosx)=2*(cos2x)/(sin2x)=2*cot2x#

Answer 2

Verify 2cot x = cot x - tan x

Explanation:

`tan 2x = (2tan x)/(1 - tan^2 x)` (Trig identity)

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

`= cot x - tan x`