Question

Using the half angle formula, what is the exact value of Cos11pi/12?

Answer 1

-
`(1)/(2)`
`\sqrt{2+√(3) }`

Explanation:

Using the half angle formula

• cos(
`(x)/(2)`) =
`\sqrt{(1+cosx)/(2) }`

here
`(x)/(2)` =
`(11\pi )/(12)`, hence

x =
`(11\pi )/(6)`

and cos (
`(11\pi )/(6)`) = cos(
`(\pi )/(6)`) =
`(√(3) )/(2)`

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

= -
`\sqrt{(1+(√(3) )/(2) )/(2) }`

= -
`\sqrt{(2+√(3) )/(4) }` = -
`(1)/(2)`
`\sqrt{2+√(3) }`