Evaluate : sin 7pi/12 . cos pi/4 - cos 7pi/12 . sin pi/4

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Solution

$We know, \sin (A - B) = \sin A \cos B - Cos A Sin B Therefore, \sin \frac{7 π}{12} \cos \frac{π}{4} - \cos \frac{7 π}{12} \sin \frac{π}{4} = \sin (\frac{7 π}{12} - \frac{π}{4}) = \sin (\frac{7 π - 3 π}{12}) = \sin (\frac{4 π}{12}) = \sin (\frac{π}{3}) = \frac{\sqrt{3}}{2} ANS . . .$

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