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Evaluate \cos 75°, leaving the answer in surd form....

Evaluate \cos 75°, leaving the answer in surd form.

A.

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

B.

\frac{\sqrt{2}}{4}(\sqrt{3} - 1)

C.

\frac{\sqrt{2}}{4}(\sqrt{3} + 1)

D.

\frac{\sqrt{2}}{2}(\sqrt{3} - 1)

Correct answer is B

\cos(a + b) = \cos a\cos b - \sin a\sin b

\cos75° = \cos(30 + 45) = (\cos30)(\cos45) - (\sin30)(\sin45)

= (\frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}) - (\frac{1}{2} \times \frac{\sqrt{2}}{2})

= \frac{\sqrt{6} - \sqrt{2}}{4}

= \frac{\sqrt{2}(\sqrt{3} - 1)}{4}