Examples Using Cos(A – B)

Some examples of using cos(A – B) formula are,

Example 1: Find the value of cos(75°).

Solution:

We can write 75° as difference of 90° and 15°.

Therefore, a = 90° and b = 15°.

Using cos(a – b) formula,

cos(75°) = cos(90° – 15°) = cos 90°.cos 15° + .sin 90°.sin 15°

Using Trigonometric Table

cos 90° = 0, cos 15° = (√3+1)/2√2, sin 90° = 1, sin 15° = (√3−1)/(2√2)

Substituting,

cos(75°) = 0.(√3+1)/2√2 + 1.(√3−1)/(2√2) = (√3−1)/(2√2)

Thus, exact value of cos(75°) = (√3−1)/(2√2)

Example 2: Find the value of cos(15°).

Solution:

We can write 15° as difference of 90° and 75°.

Therefore, a = 90° and b = 75°.

Using cos(a – b) formula,

cos(15°) = cos(90° – 75°) = cos 90°.cos 75° + .sin 90°.sin 75°

Using Trigonometric Table

cos 90° = 0, cos 75° = (√3-1)/2√2, sin 90° = 1, sin 75° = (√3+1)/(2√2)

Substituting,

cos(15°) = 0.(√3-1)/2√2 + 1.(√3+1)/(2√2) = (√3+1)/(2√2)

Thus, exact value of cos(75°) = (√3+1)/(2√2)

Formula for cos (a – b) is,

Cos(a – b) = cos a cos b + sin a sin b

Cos (a – b) is one of the important trigonometric identities, cos (a – b) is also called the cosine subtraction formula in trigonometry. Cos(a-b) is given as, cos (a – b) = cos a cos b + sin a sin b. In this article, we will learn about, cos(A – B), Proof of this Identity, How to Apply cos(A – B) Formula, and Others in detail.