Question

sin²A+sin²B+sin²C=2+2cosAcosBcosC,when A+B+C=180​

Answer 1

Answer:

Let S = sin2A + sin2B + sin2C

so that 2S = 2sin2A + 1 – cos2B +1 – cos2C

= 2 sin2A + 2 – 2cos(B + C) cos(B – C)

= 2 – 2 cos2A + 2 – 2cos(B + C) cos(B – C)

∴ S = 2 + cosA [cos(B – C) + cos(B+ C)]

since cosA = – cos(B+C)

∴ S = 2 + 2 cos A cos B cos C