Question

Prove the identity: cos(x-y)/cos x sin y = cot y + tan x

Answer 1

$\dfrac{\cos(x-y)}{\cos x\sin y}=\dfrac{\cos x\cos y+\sin x\sin y}{\cos x\sin y}=\dfrac{\cos y}{\sin y}+\dfrac{\sin x}{\cos x}=\cot y+\tan x$