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Question

Question: \[\sin 75{^\circ} =\]...

sin⁡75∘=\sin 75{^\circ} =

A

2−32\frac{2 - \sqrt{3}}{2}

B

3+122\frac{\sqrt{3} + 1}{2\sqrt{2}}

C

3−1−22\frac{\sqrt{3} - 1}{- 2\sqrt{2}}

D

3−122\frac{\sqrt{3} - 1}{2\sqrt{2}}

Answer

3+122\frac{\sqrt{3} + 1}{2\sqrt{2}}

Explanation

Solution

sin⁡75o=sin⁡(90o−15o)=cos⁡15o=cos⁡(45o−30o)\sin 75^{o} = \sin{}(90^{o} - 15^{o}) = \cos 15^{o} = \cos{}(45^{o} - 30^{o})

=3+122= \frac{\sqrt{3} + 1}{2\sqrt{2}}.