Question

Find the exact value of cos 15°

Answer 1

`(√(6) +√(2) )/(4)`

Explanation:

Answer 2

`(√(6)+√(2) )/(4)`

Explanation:

Using the difference formula for cosine and the exact values

cos45° = sin45° =
`(√(2) )/(2)`, cos30° =
`(√(3) )/(2)`, sin30° =
`(1)/(2)`

cos(a - b) = cosacosb + sinasinb

Note 15° = 45° - 30°, thus

cos15°

= cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= (
`(√(2) )/(2)` ×
`(√(3) )/(2)` ) + (
`(√(2) )/(2)` ×
`(1)/(2)` )

=
`(√(6) )/(4)` +
`(√(2) )/(4)`

=
`(√(6)+√(2) )/(4)`