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Question
In any ΔABC, prove that:
(b + c) cos A + (c + a) cos B + (a + b) cos C = a + b + c.
Sum
Solution
LHS = (b + c) cos A + (c + a) cos B + (a + b) cos C
= b cos A + c cos A + c cos B + a cos B + a cos C + b cos C
= (b cos C + c cos B) + (a cos C + c cos A) + (a cos B + b cos A)
= a + b + c ...[By projection rule]
= RHS.
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