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Starting from the left-hand side (LHS) of the identity
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$\left(1-\cos\left(x\right)\right)\left(1+\sec\left(x\right)\right)$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (1-cos(x))(1+sec(x))=sin(x)tan(x). Starting from the left-hand side (LHS) of the identity. Multiply the single term 1+\sec\left(x\right) by each term of the polynomial \left(1-\cos\left(x\right)\right). Simplify the product -(1+\sec\left(x\right)). Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}.