Question

The value of $\sin {78}^{\circ }-\sin 18+\cos {132}^{\circ }$ is

• A. $0$
• B. $1$
• C. $-1$
• D. None of these

Answer 1

The correct option is A $0$

$\begin{array}{cc}& \sin 78-\sin 18+\cos 132\\ & \sin c-\sin D=2\cos \left(\frac{c+D}{2}\right)\sin \left(\frac{c-D}{2}\right)\\ =& 2\cos \left(\frac{78+18}{2}\right)\sin \left(\frac{78-18}{2}\right)+\cos 132\\ =& 2\cos \left(48\right)\sin \left({30}^{\circ }\right)+\cos 132\\ =& 2\cos 48\times \frac{1}{2}+\cos 132\\ =& \cos 48+\cos 132\\ =& 2\cos \left(\frac{48+132}{2}\right)\cos \left(\frac{48-132}{2}\right)\\ =& 2\cos \left({90}^{\circ }\right)\cos (-18)\\ =& 2\times 0\times \cos (-18)\\ =& 0\\ & \text{option}A\text{is correct.}\end{array}$