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Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{1}{\tan\left(\theta \right)}$
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$\frac{\tan\left(x\right)+\frac{-1}{\tan\left(x\right)}}{\tan\left(x\right)+\cot\left(x\right)}$
Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (tan(x)-cot(x))/(tan(x)+cot(x)). Applying the trigonometric identity: \cot\left(\theta \right) = \frac{1}{\tan\left(\theta \right)}. Combine all terms into a single fraction with \tan\left(x\right) as common denominator. Divide fractions \frac{\frac{\tan\left(x\right)^2-1}{\tan\left(x\right)}}{\tan\left(x\right)+\cot\left(x\right)} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Multiply the single term \tan\left(x\right) by each term of the polynomial \left(\tan\left(x\right)+\cot\left(x\right)\right).