Question

If A = 60° and B = 30°, verify that cos (A – B) = cos A cos B + sin A sin B.

Answer 1

Answer:

Here is your proof.

Step-by-step explanation:

Given:  A = 60° and B = 30°

To prove: cos (A – B) = cos A cos B + sin A sin B.

Proof: Taking LHS,

cos (60 - 30) = cos 30°

cos 30° = √3 / 2

Taking RHS,

cos 60° × cos 30° + sin 60° × sin 30°

1 / 2 × √3 / 2  + √3 / 2 × 1 / 2

√3 / 4 + √3 / 4 = 2√3 / 4

= √ 3 / 2

∴ LHS = RHS

Hence proved!