Prove the trigonometric identity $\frac{1}{1-\sin\left(x\right)}+\frac{-1}{1+\sin\left(x\right)}=2\tan\left(x\right)\sec\left(x\right)$

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$\frac{1}{1-\sin\left(x\right)}+\frac{-1}{1+\sin\left(x\right)}$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity 1/(1-sin(x))+-1/(1+sin(x))=2tan(x)sec(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}. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Simplify the product -(1-\sin\left(x\right)).