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# Simplify the trigonometric expression $\frac{\frac{60}{1-2\cos\left(x\right)}}{\sin\left(x-60\right)}$

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## Derivative

$\frac{d}{dx}\left(\frac{\frac{60}{1-2\cos\left(x\right)}}{\sin\left(x-60\right)}\right)=\frac{-60\left(2\sin\left(x\right)\sin\left(x-60\right)+\left(1-2\cos\left(x\right)\right)\cos\left(x-60\right)\right)}{\left(1-2\cos\left(x\right)\right)^2\sin\left(x-60\right)^2}$ See full solution

## Integral

$\int\frac{\frac{60}{1-2\cos\left(x\right)}}{\sin\left(x-60\right)}dx=-60\ln\left(\tan\left(\frac{x}{2}\right)\right)+40\ln\left(-\frac{1}{3}+\tan\left(\frac{x}{2}\right)^2\right)+C_0$ See full solution

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### Main Topic: Simplify Trigonometric Expressions

Simplification of trigonometric expressions consists of rewriting an expression with trigonometric functions in a simpler form. To perform this task, we usually use the most common trigonometric identities, and some algebra.