Prove that the equation is an identity. cot A cot B = cot A + cot B tan A + tan B Working from the right-hand side, use the trigonometric identities for tangent and cotangent. RHS = cot A + cot B tan A + tan B COS B sin A sin A + COS B Simplify the compound fraction. RHS = sin A sin B COS A COS B = Rewrite as the product of two fractions. COS B RHS = sin A Use the trigonometric identity for tangent. cot A + cot B tan A + tan B