Question

What is the exact value of cos(11 π/12)

Answer 1

`-(1)/(4)(√(2)+√(6))`

Explanation:

`cos((11\pi)/(12))`

`cos((2\pi)/(3)+(\pi)/(4))`

`cos((2\pi)/(3))cos((\pi)/(4))-sin((2\pi)/(3))sin((\pi)/(4))`

`(-(1)/(2))((√(2))/(2))-((√(3))/(2))((√(2))/(2))`

`-(√(2))/(4)- (√(6))/(4)`

`-(1)/(4)(√(2)+√(6))`

Helpful Tips:

Sum Identity:
`cos(\alpha+\beta)=cos(\alpha)cos(\beta)-sin(\alpha)sin(\beta)`