Learn how to solve problems step by step online. Prove the trigonometric identity cot(a)-sin(2a)=cot(a)cos(2a). Starting from the left-hand side (LHS) of the identity. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right). Combine all terms into a single fraction with \sin\left(a\right) as common denominator.

Prove the trigonometric identity cot(a)-sin(2a)=cot(a)cos(2a)