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Starting from the right-hand side (RHS) of the identity
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$\left(\sin\left(x\right)+\cos\left(x\right)\right)^2$
Learn how to solve problems step by step online. Prove the trigonometric identity 1+sin(2x)=(sin(x)+cos(x))^2. Starting from the right-hand side (RHS) of the identity. Expand the expression \left(\sin\left(x\right)+\cos\left(x\right)\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1. Simplify 2\sin\left(x\right)\cos\left(x\right) using the trigonometric identity: \sin(2x)=2\sin(x)\cos(x).