Question

Find the value of cos 15°, using the result cos (A – B) = cos A cosB + sin A sin B​

Answer 1

Given , cos (A-B) = cos A cos B + sin A sin B

cos 15 = cos (45-30)

== cos 15 = cos 45 cos 30 +sin 45 sin 30

== cos 15 = 1/ root 2* root3 /2 + 1/root2 * 1/2

==cos 15 = root 3/ 2 root2 + 1/ 2 root2

== cos 15 = (root3 +1)/ 2 root2

If this wrong prefer image

Make it brainliest answer

Answer 2

cos (A - B) = cos A cos B + sin A sin B

=> Let A = 45, B = 30 (as we need A - B = 15)

=> cos (45 - 30) = cos 45 cos 30 + sin 45 sin 30.

=> cos 15 = (1/√2)(√3/2) + (1/√2)(1/2)

= (1/√2)(√3/2 + 1/2)

= (1/√2)(√3+1)/2

$= > \cos( {15}^{o} ) = \frac{ \sqrt{3} + 1}{2 \sqrt{2} }$