First slide

Compound angles

Question

$4 \sin (420 ° - α) \cos (60 ° + α) =$

Easy

A

$\sqrt{3} - 2 \sin 2 α$
B

$\sqrt{3} + 2 \cos 2 α$
C

$\sqrt{3} + 2 \sin 2 α$
D

$\sqrt{3} - 2 \cos 2 α$

Solution

$\begin{array}{l} U s e 2 \sin A \cos B = \sin (A + B) + \sin (A - B) \\ ⇒ 4 \sin (420 ° - α) \cos (60 ° + α) = 2 [\sin 480^{\circ} + \sin (360^{\circ} - 2 α)] \\ = 2 (\frac{\sqrt{3}}{2} - \sin 2 α) \\ = \sqrt{3} - 2 \sin 2 α \end{array}$

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