We have to find the value of sin 105
Solution
Sin 105° can be expressed as
sin (60° + 45°)
It is similar to sin (A + B).
We know that, the identity
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
Answer
sin 105=(√3+1)/2√2
