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 :
$$ - \frac{1}{2}$$
Solution :
The expression $$ = \left( {\sin {{78}^ \circ } - \sin {{42}^ \circ }} \right) - \left( {\sin {{66}^ \circ } - \sin {6^ \circ }} \right)$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2 \cdot \cos {60^ \circ } \cdot \sin {18^ \circ } - 2 \cdot \cos {36^ \circ } \cdot \sin {30^ \circ }$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \sin {18^ \circ } - \cos {36^ \circ }.$$ Put values and simplify.