Prove the trigonometric identity $\frac{1}{\cot\left(x\right)^2\csc\left(x\right)}=\sin\left(x\right)\tan\left(x\right)^2$

Learn how to solve problems step by step online. Prove the trigonometric identity 1/(cot(x)^2csc(x))=sin(x)tan(x)^2. Starting from the left-hand side (LHS) of the identity. Apply the trigonometric identity: \frac{1}{\csc\left(\theta \right)}=\sin\left(\theta \right). Apply the trigonometric identity: \cot(x)=\frac{\cos(x)}{\sin(x)}. Divide fractions \frac{\sin\left(x\right)}{\frac{\cos\left(x\right)^2}{\sin\left(x\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}.