Final Answer
Step-by-step Solution
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Starting from the left-hand side (LHS) of the identity
Simplify $\sqrt{\sin\left(x\right)^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{2}$
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$\frac{\sin\left(x\right)^2-\cos\left(x\right)^2}{\sin\left(x\right)+\cos\left(x\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sin(x)^2-cos(x)^2)/(sin(x)+cos(x))=sin(x)-cos(x). Starting from the left-hand side (LHS) of the identity. Simplify \sqrt{\sin\left(x\right)^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{2}. Any expression multiplied by 1 is equal to itself. Simplify \sqrt{\cos\left(x\right)^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{2}.