# CBSE Class 11-science Answered

**If A+B+C=π then prove that Cos^A+Cos^B+Cos^C=1-2CosA.CosB.CosC**

Asked by vikassuradkar2015 | 08 Dec, 2019, 11:11: PM

Expert Answer

The question which you have posted should be like this

Cos

^{2}A + Cos^{2}B + Cos^{2}C = 1- 2CosA.CosB.CosCLHS = Cos

^{2}A + Cos^{2}B + Cos^{2}C = (1 + cos 2A)/2 + (1 + cos 2B)/2 + (1 + cos 2C)/2

= 1/2 + 1/2 + 1/2 + 1/2 (cos 2A + cos 2B + cos 2C)

= 3/2 + 1/2 [2 cos (A + B) cos (A - B) + 2cos

^{2}C - 1] = 3/2 - 1/2 + 1/2 [2 cos (A + B) cos (A - B) + 2cos

^{2}C] = 1 + cos (A + B) cos (A - B) + cos

^{2}C = 1 + [-cos C cos (A - B) + cos

^{2}C] = 1 - cos C [cos (A - B) - cos C]

= 1 - cos C [cos (A - B) + cos (A + B)]

= 1 - cos C 2cos A cos B

= 1 - 2 cos A cos B cos C

= RHS

Hence,

Cos

^{2}A + Cos^{2}B + Cos^{2}C = 1- 2CosA.CosB.CosC
Answered by Sneha shidid | 09 Dec, 2019, 09:25: AM

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