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Step-by-step Solution
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Starting from the right-hand side (RHS) of the identity
Factor the polynomial $\sin\left(x\right)^2\cos\left(x\right)^2+\cos\left(x\right)^4$ by it's greatest common factor (GCF): $\cos\left(x\right)^2$
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$\sin\left(x\right)^2\cos\left(x\right)^2+\cos\left(x\right)^4$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity 1/(sec(x)^2)=sin(x)^2cos(x)^2+cos(x)^4. Starting from the right-hand side (RHS) of the identity. Factor the polynomial \sin\left(x\right)^2\cos\left(x\right)^2+\cos\left(x\right)^4 by it's greatest common factor (GCF): \cos\left(x\right)^2. Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1. Any expression multiplied by 1 is equal to itself.