Evaluate sin 105

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

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