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Starting from the left-hand side (LHS) of the identity
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$\frac{\left(\sec\left(x\right)-\tan\left(x\right)\right)^2+1}{\csc\left(x\right)\left(\sec\left(x\right)-\tan\left(x\right)\right)}$
Learn how to solve simplify trigonometric expressions problems step by step online. Prove the trigonometric identity ((sec(x)-tan(x))^2+1)/(csc(x)(sec(x)-tan(x)))=2tan(x). Starting from the left-hand side (LHS) of the identity. Rewrite \left(\sec\left(x\right)-\tan\left(x\right)\right)^2+1 in terms of sine and cosine functions. Multiply the single term \csc\left(x\right) by each term of the polynomial \left(\sec\left(x\right)-\tan\left(x\right)\right). Applying the trigonometric identity: \tan\left(\theta \right)\csc\left(\theta \right) = \sec\left(\theta \right).