Question

Evaluate cos^2 (n/12)

Answer 1

`(2+√(3) )/(4)`

Explanation:

We can use the identity
`Cos^2(x)=(1)/(2)+(1)/(2)Cos(2x)` to write it as:

`Cos^2((\pi)/(12))=(1)/(2)+(1)/(2)Cos(2((\pi)/(12)))\\=(1)/(2)+(1)/(2)Cos((\pi)/(6))\\=(1)/(2)+(1)/(2)((√(3) )/(2))\\=(1)/(2)+(√(3) )/(4)\\=(2+√(3) )/(4)`

Note: The value of
`Cos((\pi)/(6))` is
`(√(3) )/(2)`

The answer is the 2nd one,
`(2+√(3) )/(4)`