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conditional identity

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If A + B + C = π ,  show that cosA + cosB + cos C = 1 + 4 sin(A/2)sin(B/2)sin(C/2)
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start from the LHS, group a couple of terms and use cosC +cosD formula
the use B+C = π - A to change one of the factors in terms of A
change cosA using half angle formula to take out common factor
use A = π - (B+C ) to change back to B+C
again apply cosC -cosD formula
answer and  some steps are given below
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trig. formulae





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