If A + B + C = π, prove that cos 2 A + cos 2 B + cos 2 C = 1 – 2cos A cos B cos C

Question

Philoid · Accepted Answer

= cos² A + cos² B + cos² C

Using formula ,

Using ,

Using , since A + B + C = π

And, cos(π – A ) = -cosA

Using cos2A = 2cos²A -1

= 1 + cos²A – cosAcos(B-C)

= 1 + cosA{cosA - cos(B-C)}

Using ,

Since , A + B + C = π

= 1 - 2cosAcosCcosC

= R.H.S