How do you find the exact functional value sin 105° using the cosine sum or difference identity?

Sin 105° can be written as sin (60° + 45°) which is similar to sin (A + B).

We know that, the formula for sin (A + B) = sin A × cos B + cos A × sin B

Therefore, sin 105° = sin (60° + 45°) = sin 60° × cos 45° + cos 60° × sin 45°

= √3/2 × 1/√2 + 1/2 × 1/√2

= √3/2√2 + 1/2√2
= (√3+1)/2√2