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Question
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Solution
L.H.S = (cos A cos B – sin A sin B) cos C – (cos B cos C – sin B sin C) cos A
= cos A cos B cos C – sin A sin B cos C – cos A cos B cos C + cos A sin B sin C
= cos A sin B sin C – sin A sin B cos C
= sin B [sin C cos A – cos C sin A]
= sin B [sin (C – A)]
= R.H.S
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