Final Answer
Step-by-step Solution
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Starting from the left-hand side (LHS) of the identity
Applying the trigonometric identity: $1+\tan\left(\theta \right)^2 = \sec\left(\theta \right)^2$
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$\cos\left(x\right)\left(1+\tan\left(x\right)^2\right)$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity cos(x)(1+tan(x)^2)=sec(x). Starting from the left-hand side (LHS) of the identity. Applying the trigonometric identity: 1+\tan\left(\theta \right)^2 = \sec\left(\theta \right)^2. Apply the trigonometric identity: \cos\left(\theta \right)\sec\left(\theta \right)^n=\sec\left(\theta \right)^{\left(n-1\right)}, where n=2. Since we have reached the expression of our goal, we have proven the identity.