The value of 78^ - 66^ - 42^ + 6^ is - Vidyadip

MCQ

The value of $\sin78^\circ-\sin66^\circ-\sin42^\circ+\sin6^\circ\text{ is }$

A
$\frac{1}{2}$
✓
$-\frac{1}{2}$
C
$-1$
D
None of these

✓

Answer

Correct option: B.

$-\frac{1}{2}$

$\sin(60^\circ+18^\circ)-\sin(60^\circ-18^\circ)-(\sin66^\circ-\sin6^\circ)$
$=\ \sin60^\circ\cos18^\circ+\cos60^\circ\sin18^\circ-\sin60^\circ\cos18^\circ\\ \ \ \ +\cos60^\circ\sin18^\circ-(2\cos36^\circ\frac{1}{2})$
$=\ 2\times\frac{1}{2}\cos18^\circ-\cos36^\circ$
$=\ \frac{\sqrt5-1}{4}-\frac{\sqrt5+1}{4}$
$=\ \frac{-2}{4}$
$=\ \frac{-1}{2}$

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