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Starting from the left-hand side (LHS) of the identity
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$\csc\left(x\right)-\sin\left(x\right)$
Learn how to solve problems step by step online. Prove the trigonometric identity csc(x)-sin(x)=cot(x)cos(x). Starting from the left-hand side (LHS) of the identity. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Combine all terms into a single fraction with \sin\left(x\right) as common denominator. Apply the trigonometric identity: 1-\sin\left(\theta \right)^2=\cos\left(\theta \right)^2.