MCQ
$sin78^0 - sin66^0 - sin42^0 + sin6^0 = ......$
- A$\frac{1}{2}$
- ✓$-\frac{1}{2}$
- C$2$
- D$-2$
$sin78^0 - sin 66^0 - sin42^0 + sin6^0$
$= \left(sin78^0 - sin42^0\right) - \left(sin66^0 - sin6^0\right) $
$= 2 cos60^0 \ sin18^0 - 2cos36^0 \ sin30^0$
$= 2sin 18^0 \ \frac{1}{2} - 2cos36^0 \frac{1}{2}$
$= sin 18^0 - cos36^0$
$= \frac{\sqrt{5} - 1}{4} - \frac{\sqrt{5} + 1}{4}$
$= \frac{\sqrt{5} - 1 - \sqrt{5 }- 1}{4}$
$ = \frac{-2}{4}$
$ = -\frac{1}{2}$
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