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 = $$\sqrt{3} + 1\over 2\sqrt{2}$$