Prove the trigonometric identity $\cos\left(b\right)^2\left(\sec\left(b\right)^2-1\right)=\sin\left(b\right)^2$

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$\cos\left(b\right)^2\left(\sec\left(b\right)^2-1\right)$

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity cos(b)^2(sec(b)^2-1)=sin(b)^2. Starting from the left-hand side (LHS) of the identity. Apply the trigonometric identity: \sec\left(\theta \right)^2-1=\tan\left(\theta \right)^2, where x=b. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\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}.