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Starting from the left-hand side (LHS) of the identity
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$\frac{1+\cos\left(x\right)}{1-\cos\left(x\right)}+\frac{-\left(1-\cos\left(x\right)\right)}{1+\cos\left(x\right)}$
Learn how to solve problems step by step online. Prove the trigonometric identity (1+cos(x))/(1-cos(x))+(-(1-cos(x)))/(1+cos(x))=4cot(x)csc(x). Starting from the left-hand side (LHS) of the identity. Simplify the product -(1-\cos\left(x\right)). 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(1-\cos\left(x\right)\right)\left(1+\cos\left(x\right)\right).