Learn how to solve differential calculus problems step by step online. Prove the trigonometric identity (2cos(2x))/sin(2x)=1/tan(x)-tan(x). Starting from the right-hand side (RHS) of the identity. Combine all terms into a single fraction with \tan\left(x\right) as common denominator. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Divide fractions \frac{1-\tan\left(x\right)^2}{\frac{\sin\left(x\right)}{\cos\left(x\right)}} 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}.

Prove the trigonometric identity (2cos(2x))/sin(2x)=1/tan(x)-tan(x)