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Prove that : a cos A +b cos B+ c cos C=2 a sin B sin C

Posted by Singh Rajput 5 years, 3 months ago

CBSE > Class 11 > Mathematics

1 answers

Ram Kushwah 5 years, 3 months ago

We know     a / sin A = b / sin B = c / sin C.
                   b = a cos C + c Cos A
                   c = a Cos B + b cos A

LHS = a cos A + (a cos C + c cos A) cos B + (a cos B + b Cos A) cos C
        = a cos A + cos A (c cos B + b Cos C) + 2 a Cos C Cos B
        = a cos A + cos A * a + 2 a cos C cos B
        = 2a [cos A + Cos C Cos B]
        = 2 a [ cos (π-B-C) + cos C cos B]
        = 2 a [- cos (B+C) + cos C cos B]
        = 2 a Sin B sin C

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CBSE > Class 11 > Mathematics