Prove the trigonometric identity $\sin\left(x\right)^2\cos\left(y\right)+\cos\left(x\right)^2\cos\left(y\right)=\cos\left(y\right)$

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$\sin\left(x\right)^2\cos\left(y\right)+\cos\left(x\right)^2\cos\left(y\right)$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sin(x)^2cos(y)+cos(x)^2cos(y)=cos(y). Starting from the left-hand side (LHS) of the identity. Factor the polynomial \sin\left(x\right)^2\cos\left(y\right)+\cos\left(x\right)^2\cos\left(y\right) by it's greatest common factor (GCF): \cos\left(y\right). Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1. Since we have reached the expression of our goal, we have proven the identity.