Question

Prove cot u - cot 2u=cosec 2u?

Answer 1

cotu - cot2u
= cotu - (cot^2u-1)/2cotu
= (2cot^2u-cot^2u+1)/2cotu
= (cot^2u+1)/2cotu
= (cos^2u+sin^2u)/(2cosu sinu)
= 1/sin2u
= csc2u