Find the value of cos 15 using cos (A - B) identity.

We can find the value of cos 15° using cos (A - B) identity.

Answer: The value of cos 15° = (√3+1)/2√2

Let see, how we can find the value of cos 15°

Explanation: 

We have to find the value of cos 15 using cos (A - B) identity.

cos 15° can be written as cos 15 = cos (45° – 30°)       ------- (1)

Now, we need to apply the formula cos (A – B) = cos A. cos B + sin A. sin B

cos (45° – 30°) = cos 45°. cos 30° + sin 45°. sin 30°   ------ (2)

We know that sin 45° = 1/√2, cos 45° = 1/√2, sin 30° = 1/2, cos 30° = √3/2

Substitute the value of sin 30°, sin 45°, cos 30° and cos 45°, then equation (2) will become

cos (45° – 30°) = 1/√2 . √3/2 + 1/√2 . 1/2

cos 15° = √3/2√2 + 1/2√2

cos 15° = (√3+1)/2√2

Thus, the value of  cos 15° = (√3+1)/2√2