• question_answer $\sin 47{}^\circ +\sin 61{}^\circ -\sin 11{}^\circ -\sin 25{}^\circ$ is equal to A) $\sin 36{}^\circ$ B) $\cos 36{}^\circ$ C) $\sin 7{}^\circ$ D) $\cos 7{}^\circ$

 The given expression is equal to $(\sin 47{}^\circ +\sin 61{}^\circ )-(sin11{}^\circ +sin25{}^\circ )$$=2\sin 54{}^\circ \cos 7{}^\circ -2\sin 18{}^\circ \cos 7{}^\circ$$=2\cos 7{}^\circ \,(\sin 54{}^\circ -\sin 18{}^\circ )$ $=2\,\cos 7{}^\circ \left[ \frac{\sqrt{5}+1}{4}-\frac{\sqrt{5}-1}{4} \right]=\cos 7{}^\circ$