Final answer to the problem
Step-by-step Solution
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Starting from the left-hand side (LHS) of the identity
Applying an identity of double-angle cosine: $\cos\left(2\theta\right)=1-2\sin\left(\theta\right)^2$
Learn how to solve trigonometric identities problems step by step online.
$\sin\left(x\right)^2+\cos\left(2x\right)$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sin(x)^2+cos(2x)=cos(x)^2. Starting from the left-hand side (LHS) of the identity. Applying an identity of double-angle cosine: \cos\left(2\theta\right)=1-2\sin\left(\theta\right)^2. Combining like terms \sin\left(x\right)^2 and -2\sin\left(x\right)^2. Apply the trigonometric identity: 1-\sin\left(\theta \right)^2=\cos\left(\theta \right)^2.