Question

$\frac{1}{4}\left[\sqrt{3}\cos 23^{\circ }-\sin 23^{\circ }\right]=$

• A. $\cos 43^{\circ }$
• B. $\cos 7^{\circ }$
• C. $\cos 53^{\circ }$
• D. None of these

Answer 1

Answer: (D)

$\frac{1}{4}\left\{\sqrt{3}\cos 23^{\circ }-\sin 23^{\circ }\right\}$
$=\frac{1}{2}\left\{\cos 30^{\circ }\cos 23^{\circ }-\sin 30^{\circ }\sin 23^{\circ }\right\}$
$=\frac{1}{2}\cos \left\{30^{\circ }+23^{\circ }\right\}=\frac{1}{2}\cos 53^{\circ }$