Sin 165° = sin (120° + 45°) =sin 120°.cos45° + cos120° . Sin45° =sin(180°-60°).cos45° - cos(180°-60°) . Sin 45° = sin60° . Cos 45° - cos 60° . Sin 45° =1/2√3. 1/2√2 - 1/2 . 1/2√2 =1/4√6 - 1/4√2 =1/4(√6-√2)
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Sin 165° = sin (120° + 45°)
=sin 120°.cos45° + cos120° . Sin45°
=sin(180°-60°).cos45° - cos(180°-60°) . Sin 45°
= sin60° . Cos 45° - cos 60° . Sin 45°
=1/2√3. 1/2√2 - 1/2 . 1/2√2
=1/4√6 - 1/4√2
=1/4(√6-√2)