Learn how to solve problems step by step online. Prove the trigonometric identity (1-sin(x)^2)/cot(x)=sin(x)cos(x). Starting from the left-hand side (LHS) of the identity. Since the trigonometric functions \cot and \tan are reciprocal, we can simplify \frac{1-\sin\left(x\right)^2}{\cot\left(x\right)} into . Apply the trigonometric identity: 1-\sin\left(\theta \right)^2=\cos\left(\theta \right)^2. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}.

Prove the trigonometric identity (1-sin(x)^2)/cot(x)=sin(x)cos(x)