Prove that: i. ii. cos (A + B + C) + cos (A – B + C) + cos (A + B – C) + cos (-A + B + C) = 4 cos A cos B cos C

Question

Philoid · Accepted Answer

Take L.H.S:

{sin (-A) = - sin A}

= R.H.S.

Hence Proved

ii. Take L.H.S.:

cos(A + B + C) + cos (A – B + C) + cos(A + B – C) + cos(-A + B + C)

= {cos (A + B + C) + cos (A – B + C)} + {cos (A + B – C) + cos (-A + B + C)}

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

= 2 cos B {cos (A + C) + cos (A – C)}

= 4 cos A cos B cos C

= R.H.S.

Hence Proved