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in any triangle, show that sin(A + B + C) = sinAcosBcosC + sinBcosAcosC + sinCcosAcosB, where A, B, C : are angles.
Dear Student Use the formula sin(a + b) = sina cosb + sinb cos a Then sin(a + b + c) = sin((a + b) + c) = sin(a + b) cosc + cos(a + b) sin c Then use the formula cos(a + b) = cosa cosb - sina sinb to get sin(a + b) cosc + cos(a + b) sin c = (sina cosb + sinb cosa) cosc + (cosa cosb - sina sinb) sinc = sina cosb cosc + sinb cosa cosc + sinc cosa cosb - sina sinb sinc RegardsArun (askIITians forum expert)
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