Question

cotx+tan2x=cotxsec2x
prove

Answer 1

cosx/sinx + 2sinxcosx/cos2x
= (cosxcos2x + 2sin^2(x) cosx)/(sinxcos2x)
= cotxsec2x (cos2x + 2sin^2(x))
= cotx sec2x (1-2sin^2(x) + 2sin^2(x))
= cotx sec2x