Question

$\frac{1}{4}[\sqrt{3}\cos {23}^{\circ }-\sin {23}^{\circ }]$ is equal to

• A. $\frac{1}{2}\cos {43}^{\circ }$
• B. $\frac{1}{2}\cos 7^{\circ }$
• C. $\frac{1}{2}\cos {53}^{\circ }$
• D. none of these

Answer 1

The correct option is C $\frac{1}{2}\cos {53}^{\circ }$

$\frac{1}{2}[\frac{\sqrt{3}cos{23}^0}{2}-\frac{1.sin{23}^0}{2}]$
$=\frac{1}{2}[cos{30}^{0}cos{23}^0-sin{30}^{0}sin{23}^0]$
$=\frac{1}{2}\left[cos\right({30}^0+{23}^0\left)\right]$
$=\frac{1}{2}cos\left({53}^0\right)$