# Step-by-step Solution

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## Step-by-step solution

Problem to solve:

$\frac{\cos\left(x\right)}{1-\sin\left(x\right)}-\frac{\cos\left(x\right)}{1+\sin\left(x\right)}=2\tan\left(x\right)$

Solving method

Learn how to solve trigonometric identities problems step by step online.

$\frac{\cos\left(x\right)}{1-\sin\left(x\right)}+\frac{-\cos\left(x\right)}{1+\sin\left(x\right)}=2\tan\left(x\right)$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (cos(x)/(1-sin(x))-(cos(x)/(1+sin(x))=2tan(x). Multiplying the fraction by -1. 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 -(1-\sin\left(x\right)). Factoring by \cos\left(x\right).

$\frac{\cos\left(x\right)}{1-\sin\left(x\right)}-\frac{\cos\left(x\right)}{1+\sin\left(x\right)}=2\tan\left(x\right)$