Question

The value of `cos^2x + cos^2(x + π/3) + cos^2(π - (2π)/3)` is ______.

Options

• `3/2`

• `4/3`

• `3/4`

• `2/3`

Answer 1

The value of `cos^2x + cos^2(x + π/3) + cos^2(π - (2π)/3)` is `underlinebb(3/2)`.

Explanation:

`cos^2x + cos^2(x + π/3) + cos^2(π - (2π)/3)`

= `(1 + cos 2x)/2 + (1 + cos 2(x + π/3))/2 + (1 + cos2(x - (2π)/3))/2`

= `1/2[3 + cos 2x + cos(2x + (2π)/3) + cos(2x - (2π)/3)]`

= `1/2[3 + cos 2x + 2 cos 2x cos  (2π)/3]`

= `1/2[3 + cos 2x + 2 cos 2x cos(π - (2π)/3)]`

= `1/2[3 + cos 2x - 2 cos 2x cos  π/3]`

= `1/2[3 + cos 2x - cos 2x]`

= `3/2`