Question -
Answer -
Let us consider LHS:
(cos α + cos β)2 + (sin α + sin β)2
Upon expansion, we get,
(cos α + cos β)2 + (sin α + sin β)2 =
= cos2 α + cos2 β + 2cos α cos β + sin2 α + sin2 β + 2 sin α sin β
= 2 + 2 cos α cos β + 2 sin α sin β
= 2 (1 + cos α cos β + sin α sin β)
= 2 (1 + cos (α – β)) [since, cos (A – B) = cos A cosB + sin A sin B]
= 2 (1 + 2 cos2 (α – β)/2 – 1) [since,cos2x = 2cos2 x – 1]
= 2 (2 cos2 (α – β)/2)
= 4 cos2 (α – β)/2
= RHS
Hence Proved.