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Starting from the left-hand side (LHS) of the identity
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$\frac{1}{\sec\left(x\right)-1}+\frac{1}{\sec\left(x\right)+1}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity 1/(sec(x)-1)+1/(sec(x)+1)=2csc(x)cot(x). Starting from the left-hand side (LHS) of the identity. Combine fractions with different denominator using the formula: \displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}. Solve the product of difference of squares \left(\sec\left(x\right)-1\right)\left(\sec\left(x\right)+1\right). Apply the trigonometric identity: \sec\left(\theta \right)^2-1=\tan\left(\theta \right)^2.