Trigonometric Identities Question 357

Question: $ \sin 75{}^\circ = $

[MNR 1979]

Options:

A) $ \frac{2-\sqrt{3}}{2} $

B) $ \frac{\sqrt{3}+1}{2\sqrt{2}} $

C) $ \frac{\sqrt{3}-1}{-2\sqrt{2}} $

D) $ \frac{\sqrt{3}-1}{2\sqrt{2}} $

Show Answer

Answer:

Correct Answer: B

Solution:

$ \sin ,75^{o}=\sin (90^{o}-15^{o})=\cos ,15^{o}=\cos (45^{o}-30^{o}) $ $ =\frac{\sqrt{3}+1}{2\sqrt{2}} $ .