A) \[\sin 36{}^\circ \]
B) \[\cos 36{}^\circ \]
C) \[\sin 7{}^\circ \]
D) \[\cos 7{}^\circ \]
Correct Answer: D
Solution :
\[\sin \,\,{{47}^{o}}+\sin \,\,{{61}^{o}}-(\sin \,\,{{11}^{o}}+\sin \,\,{{25}^{o}})\] \[=\frac{\sin \,\,{{20}^{o}}\sin \,\,{{40}^{o}}\sin \,\,{{80}^{o}}}{\cos \,\,{{20}^{o}}\cos \,\,{{40}^{o}}\cos \,\,{{80}^{o}}}\] \[=\,\,2\,\,\cos \,\,{{7}^{o}}\,(\sin \,\,{{54}^{o}}-\sin \,\,{{18}^{o}})\] \[=\,\,2\,\,\cos \,\,{{7}^{o}}\,\,.\,\,2\,\,\cos \,\,{{36}^{o}}\,\,.\,\,\sin \,\,{{18}^{o}}\] \[=\,\,4.\,\cos \,\,{{7}^{o}}.\,\frac{\sqrt{5}+1}{4}.\frac{\sqrt{5}-1}{4}=\cos \,\,{{7}^{o.}}\].
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