Question

3. Prove that:
(1) 2 cos 45º cos 15° = √3 + 1/2​

Answer 1

Step-by-step explanation:

$\cos( x) + \cos(y) = 2 \cos( \frac{x + y}{2} ) \cos( \frac{x - y}{2} )$

Using the above formula we know that

(x+y)/2 =45°=>x+y =90° and (x-y)/2 =15° =>x-y =30° and so (x+y)+(x-y)= 90°+30° =>2x=120°=>x=60° and 60°+y=90° =>y=30°.

2cos(45°)cos(15°) =>cos(60°)+cos(30°) =>

1/2 +√3/2 => (√3+1)/2. Hope it helps you.