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Question
Prove that:
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Solution
LHS =
\[\sin\left( \frac{3\pi}{8} - 5 \right)\cos\left( \frac{\pi}{8} + 5 \right) + \cos\left( \frac{3\pi}{8} - 5 \right)\sin\left( \frac{\pi}{8} + 5 \right)\]
\[ = \sin\left[ \left( \frac{3\pi}{8} - 5 \right) + \left( \frac{\pi}{8} + 5 \right) \right] \left[ \sin A\cos B + \cos A\sin B = \sin\left( A + B \right) \right]\]
\[ = \sin\frac{4\pi}{8}\]
\[ = \sin\frac{\pi}{2}\]
\[ = 1\]
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