Final Answer
Step-by-step Solution
Specify the solving method
Starting from the left-hand side (LHS) of the identity
Multiply the single term $1-\sin\left(x\right)$ by each term of the polynomial $\left(\sec\left(x\right)+\tan\left(x\right)\right)$
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$\left(\sec\left(x\right)+\tan\left(x\right)\right)\left(1-\sin\left(x\right)\right)$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sec(x)+tan(x))(1-sin(x))=cos(x). Starting from the left-hand side (LHS) of the identity. Multiply the single term 1-\sin\left(x\right) by each term of the polynomial \left(\sec\left(x\right)+\tan\left(x\right)\right). Multiply the single term \sec\left(x\right) by each term of the polynomial \left(1-\sin\left(x\right)\right). Applying the trigonometric identity: \sin\left(\theta \right)\sec\left(\theta \right) = \tan\left(\theta \right).