Prove the trigonometric identity $\sin\left(u\right)^2\left(1+\cot\left(u\right)^2\right)=1$

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$\sin\left(u\right)^2\left(1+\cot\left(u\right)^2\right)$

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity sin(u)^2(1+cot(u)^2)=1. Starting from the left-hand side (LHS) of the identity. Apply the trigonometric identity: 1+\cot\left(\theta \right)^2=\csc\left(\theta \right)^2, where x=u. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}.