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Rewrite $\tan\left(x\right)-\cot\left(x\right)$ in terms of sine and cosine functions
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$\frac{\frac{\sin\left(x\right)^2-\cos\left(x\right)^2}{\cos\left(x\right)\sin\left(x\right)}}{\tan\left(x\right)+\cot\left(x\right)}$
Learn how to solve problems step by step online. Simplify the trigonometric expression (tan(x)-cot(x))/(tan(x)+cot(x)). Rewrite \tan\left(x\right)-\cot\left(x\right) in terms of sine and cosine functions. Simplify \cos\left(x\right)\sin\left(x\right) using the trigonometric identity: \sin(2x)=2\sin(x)\cos(x). Divide fractions \frac{\sin\left(x\right)^2-\cos\left(x\right)^2}{\frac{\sin\left(2x\right)}{2}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Applying the trigonometric identity: \sin\left(\theta \right)^2-\cos\left(\theta \right)^2 = -\cos\left(2\theta \right).