Answer:
(√6 +√2)/4
Step-by-step explanation:
You want the exact value of cos(15°).
Trig identity
The difference of angles formula is ...
cos(α-β) = cos(α)cos(β) +sin(α)sin(β)
Application
This value for cos(15°) can be found as ...
cos(15°) = cos(45° -30°)
cos(15°) = cos(45°)cos(30°) +sin(45°)sin(30°)
= (√2/2)(√3/2) +(√2/2)(1/2) = (√6 +√2)/4
The exact value of cos(15°) is (√6 +√2)/4.
__
Additional comment
Using the half-angle identity, cos(θ/2) = √((1+cos(θ))/2), you get ...
cos(15°) = √((1 +cos(30°))/2) = √((1 +√3/2)/2) = √((2+√3)/4)
cos(15°) = √(2+√3)/2
One can simplify this square root by writing it as ...
cos(15°) = √((8+2√3)/16) = √((√6 +√2)²/16) = (√6 +√2)/4
