Discussion

The value of \(\sin 75°\) is:

Answer: A

We can write 75° as the sum of two standard angles, 45° + 30°.

Using the sine addition formula: \(\sin(A+B) = \sin A \cos B + \cos A \sin B\).

\(\sin(45°+30°) = \sin 45° \cos 30° + \cos 45° \sin 30°\)

= \((\frac{1}{\sqrt{2}})(\frac{\sqrt{3}}{2}) + (\frac{1}{\sqrt{2}})(\frac{1}{2})\)

= \(\frac{\sqrt{3}}{2\sqrt{2}} + \frac{1}{2\sqrt{2}} = \frac{\sqrt{3}+1}{2\sqrt{2}}\).

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