If (cos α + cos β)2 + (sin α + sin β)2 write the value of λ.
(cos α + cos β)2 + (sin α + sin β)2
= (cos2 α + 2cos α cos β + cos2 β) + (sin2 α + 2sin α sin β + sin2 β)
Rearranging the terms,
= (cos2 α + sin2 α) + (cos2 β + sin2 β) + 2(cos α cos β + sin α sin β)
= 1 + 1 + 2cos (α – β)
= 2{1 + cos (α – β)}
=
= 4cos2
Comparing with question, λ = 4 (Ans)