Question

The value of $\sin {78}^{\circ }-\sin {66}^{\circ }-\sin {42}^{\circ }+\sin 6^{\circ }$ is

• A. $\frac{1}{2}$
• B. $-\frac{1}{2}$
• C. $-1$
• D. none of these

Answer 1

The correct option is B $-\frac{1}{2}$

$\sin {78}^{\circ }-\sin {66}^{\circ }-\sin {42}^{\circ }+\sin 6^{\circ }$
$=(\sin {78}^{\circ }-\sin {42}^{\circ })+(\sin 6^{\circ }-\sin {66}^{\circ })$
$=2\sin 18\cos 60+2\sin (-30)\cos 36$
$=\sin 18-\cos 36$
$=\frac{\sqrt{5}-1}{4}-\frac{\sqrt{5}+1}{4}$
$=-\frac{1}{2}$