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Starting from the left-hand side (LHS) of the identity
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$\left(\sec\left(x\right)+\tan\left(x\right)\right)\left(\sec\left(x\right)-\tan\left(x\right)\right)$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sec(x)+tan(x))(sec(x)-tan(x))=1. Starting from the left-hand side (LHS) of the identity. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Applying the trigonometric identity: \sec\left(\theta \right)^2 = 1+\tan\left(\theta \right)^2. Cancel like terms \tan\left(x\right)^2 and -\tan\left(x\right)^2.