Question

confirm the identity 2cot2x=cotx-tanx

Answer 1

Put in terms of tan:
= 2 / tan(2x)
Double angle trig identity:
= 2 / [2tan(x) / [1 - tan^2(x)]]
Divide the fractions:
= [2(1 - tan^2(x))] / 2tan(x)
Divide numerator and denominator by 2:
= (1 - tan^2(x)) / tan(x)
Separate into two fractions:
= 1/tan(x) - tan^2(x)/tan(x)
Simplify:
= cot(x) - tan(x)