The value of `sin 78^0-sin 66^0-sin 42^0+sin6^0` is `-1` b. `1//2` c. `-1//2` d. none of these

Explanation

`sin 78^{circ}-sin 66^{circ}-sin 42^{circ}+sin 6^{circ}`


`=(sin 78^{circ}-sin 42^{circ})+(sin 6^{circ}-sin 66^{circ})`


`=2 sin 18 cos 60+2 sin (-30) cos 36`


`=sin 18-cos 36`


`=frac{sqrt{5}-1}{4}-frac{sqrt{5}+1}{4}`


`=-frac{1}{2}`