Verify the identity. $$\frac{\sin(8x)-\sin(2x)}{\cos(8x)-\cos(2x)}=-\cot(5x)$$ Start with the numerator of the left side and apply the appropriate formula of sum-to-product. $$\sin(8x)-\sin(2x)=\boxed{2\cos(5x)\sin(3x)}$$ (Do not simplify.)
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Step 1: The sum-to-product formula for sine is: $$\sin(A)-\sin(B)=2\cos\left(\frac{A+B}{2}\right)\sin\left(\frac{A-B}{2}\right)$$ Show more…
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