Find the Value of Sin 15 Degrees ?

Solution :

The value of sin 15 degrees is \(\sqrt{3} – 1\over 2\sqrt{2}\).

Proof :

We will write sin 15 as sin (45 – 30).

By using formula sin (A – B) = sin A cos B – cos A sin B,

sin (45 – 30) = sin 45 cos 30 – cos 45 sin 30

\(\implies\) sin 15 = \(1\over \sqrt{2}\) \(\times\) \(\sqrt{3}\over 2\) – \(1\over \sqrt{2}\) \(\times\) \(1\over 2\)

\(\implies\) sin 15 = \(\sqrt{3} – 1\over 2\sqrt{2}\)

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