Final answer to the problem
Step-by-step Solution
Specify the solving method
Starting from the left-hand side (LHS) of the identity
Combine fractions with different denominator using the formula: $\displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}$
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$\frac{\cos\left(x\right)}{\sec\left(x\right)-1}+\frac{\cos\left(x\right)}{\sec\left(x\right)+1}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity cos(x)/(sec(x)-1)+cos(x)/(sec(x)+1)=2cot(x)^2. 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). Expand the expression \cos\left(x\right)\left(\sec\left(x\right)+1\right)+\cos\left(x\right)\left(\sec\left(x\right)-1\right) completely and simplify.