Question

prove that cos²○+cos²(○+120°)+cos²(○-120°)=³/²​

Answer 1

Answer:

3/2

Step-by-step explanation:

Cos²θ + Cos²(θ+120) + Cos²(θ-120)

= 1 + Cos2θ/2 +1 + Cos2(θ+120) /2 + 1 + Cos2(θ-120) /2

3/2 + 1/2[Cos2θ + Cos(2θ+240)+Cos(2θ-240)]

= 3/2 + 1/2(Cos2θ + 2Cos2θCos240°)

= 3/2 + 1/2(Cos2θ + 2Cos2θCos(180+60))

= 3/2 + 1/2(Cos2θ + 2Cos2θCos(-60))

= 3/2+1/2(Cos2θ - Cos2θ)

= 3/2 + 0

= 3/2.