Question

Find the value :
$\sin {78}^{\circ }-\sin {18}^{\circ }+\sin {30}^{\circ }-\sin {42}^{\circ }$

• A. $\frac{3}{2}$
• B. $\frac{1}{2}$
• C. $\frac{5}{2}$
• D. None of these

Answer 1

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

$sin\left(78\right)-sin\left(18\right)+sin\left(30\right)-sin\left(42\right)$

$=sin\left(78\right)-sin\left(42\right)-sin\left(18\right)+sin\left(30\right)$

$=2cos\left(\frac{120}{2}\right)sin\left(18\right)-sin\left(18\right)+sin\left(30\right)$

$=2\times \frac{1}{2}sin\left(18\right)-sin\left(18\right)+sin30$

$=sin30$

$=\frac{1}{2}$