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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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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Find the derivative
• Integrate using basic integrals
• Verify if true (using algebra)
• Verify if true (using arithmetic)
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
• Integrate by parts
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##  Final answer to the problem

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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 step-by-step 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 step-by-step solution

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

###  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.