Find the Value of Sin 75 Degrees ?

Solution :

The value of sin 75 degrees is \(\sqrt{3} + 1\over 2\sqrt{2}\).

Proof :

We will write sin 75 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 75 = \(1\over \sqrt{2}\) \(\times\) \(\sqrt{3}\over 2\) + \(1\over \sqrt{2}\) \(\times\) \(1\over 2\)

\(\implies\) sin 75 = \(\sqrt{3} + 1\over 2\sqrt{2}\)

Leave a Comment

Your email address will not be published.