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

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$\frac{\sin\left(x\right)^2}{\cos\left(x\right)^2}$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity tan(x)^2=(sin(x)^2)/(cos(x)^2). Starting from the right-hand side (RHS) of the identity. Apply the property of the quotient of two powers with the same exponent, inversely: \frac{a^m}{b^m}=\left(\frac{a}{b}\right)^m, where m equals 2. Apply the trigonometric identity: \frac{\sin\left(\theta \right)}{\cos\left(\theta \right)}=\tan\left(\theta \right). Since we have reached the expression of our goal, we have proven the identity.