# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

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

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

Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation (1-cos(x))/(sin(x)-(sin(x)/(1-cos(x))=2csc(x)*cot(x). Multiplying the fraction by -1. Grouping terms. Unifying fractions with different denominator. Multiplying polynomials \sin\left(x\right) and 1-\cos\left(x\right).

$x=\frac{\pi}{2},\:x=-\frac{\pi}{2}$

### Problem Analysis

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

### Main topic:

Trigonometric Equations

~ 2.55 seconds