Question

prove the identity
ctgx+ctgy= sin(x+y)/sinx × siny​

Answer 1

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