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I. Express the LHS in terms of sine and cosine and simplify
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Learn how to solve problems step by step online. Prove the trigonometric identity (sin(x)+cos(x))^2+(sin(x)-cos(x))^2=2. section:I. Express the LHS in terms of sine and cosine and simplify. Start from the LHS (left-hand side). A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: (a-b)^2=a^2-2ab+b^2. Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1.