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Starting from the left-hand side (LHS) of the identity
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$\frac{\csc\left(x\right)}{1+\csc\left(x\right)}+\frac{-\csc\left(x\right)}{1-\csc\left(x\right)}$
Learn how to solve problems step by step online. Prove the trigonometric identity csc(x)/(1+csc(x))+(-csc(x))/(1-csc(x))=2sec(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}. Simplify the product -(1+\csc\left(x\right)). Solve the product of difference of squares \left(1+\csc\left(x\right)\right)\left(1-\csc\left(x\right)\right).