Question

PLEASE HELP ME!!! I don’t understand

Answer 1

see explanation

Explanation:

Using the addition formula for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

and exact values

sin45° = cos45° =
`(√(2) )/(2)`

c0s30° =
`(√(3) )/(2)` , sin30° =
`(1)/(2)`

Express cos15° = cos(45 - 30 )°, then

cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

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

=
`(√(6) )/(4)` +
`(√(2) )/(4)`

=
`(√(6)+√(2)  )/(4)` ← exact value

Answer 2

√6 + √2

= --------------

4

Explanation:

15° = 45° - 30°

So

cos(15) = cos(45 - 30)

=cos(45) × cos(30) + sin(45) × sin(30)

= 1/√2 × (√3)/2 + 1/√2 × 1/2

(√3) + 1

= --------------

2√2

(√3) + 1 √2

= -------------- x ---------

2√2 √2

√6 + √2

= --------------

4