Question

Prove that cos^2 a+cos^2 (a+2 pie/3) + cos^2 (a-2pie/3) =3

Answer 1

LHS =======================

Cos^2a + Cos^2(a +2pie/3) + Cos^2(a-2pie/3)

= (1+cos a) 1/2 + (1+cos(a+2pie/3)) 1/2 + (1+cos(a-2 pie/3)) 1/2

= 1/2 ( 1+cos a + 1 +Cos(a+2 pie/3) + 1 + Cos(a -2 pie/3) )

= 1/2 ( 3 + cos a + Cos( a + 120 ) + Cos( a - 120)

. = 1/2 ( 3 + Cos a + 2 cos a cos120)

= 1/2 ( 3 + cos a + 2 cos a . -1/2)

(since cos 120 = -1/2)

= 1/2× ( 3 + cosa - cosa)
=> 3/2
= = RHS