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

2 Answers

We have that

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

Nov 4, 2015

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