Establish the identity sinalpha betasin alpha beta cot be

Establish the identity. sin(alpha - beta)/sin (alpha + beta) = cot beta - cot alpha/cot beta + cot alpha

Solution

LHS = sin( - )/sin( + ) = [sin()cos() – cos()sin()]/[sin()cos() + cos()sin()]

Multiplying and divide by sin()sin(), we get

sin( - )/sin( + ) = [cot() – cot()]/[cot() + cot()] = RHS