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Question

If sin(A - B) = sinA cos B - cosA sinB and cos(A - B)= cos A cos B + sin Asin B then find
sin15 and cos 15 .

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Solution

sin (A - B) = Sin A Cos B - Cos A sin B

Let A = 45° and
​​​ B = 30°

sin (45° - 30°) = Sin 45° Cos 30° - Cos 45° sin 30°

sin (45° - 30°) = (1/√2)(√3/2) - (1/√2)(1/2)

sin 15° = (√3 - 1) / (2√2)



cos (A - B) = Cos A Cos B + Sin A sin B

Let A = 45° and B = 30°

cos (45° - 30°) = Cos 45° Cos 30° + Sin 45° sin 30°

cos (45° - 30°) = (1/√2)(√3/2) + (1/√2)(1/2)

cos 15° = (√3 + 1) / (2√2)

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