A) \[\frac{1}{2}\]
B) 1
C) \[-\frac{1}{2}\]
D) \[\frac{1}{8}\]
Correct Answer: C
Solution :
\[\cos \,\,{{12}^{o}}+\cos \,\,{{84}^{o}}+\cos \,\,{{156}^{o}}+\cos \,\,{{132}^{o}}\] \[=(\cos \,\,{{12}^{o}}+\cos \,\,{{132}^{o}})+(\cos \,\,{{84}^{o}}+\cos \,\,{{156}^{o}})\] \[=2\,\,\cos {{72}^{o}}\cos \,{{60}^{o}}+2\cos \,\,{{120}^{o}}\cos \,\,{{36}^{o}}\] \[=2\,\left[ \cos \,\,{{72}^{o}}\times \frac{1}{2}-\frac{1}{2}\times \cos \,\,{{36}^{o}} \right]\] \[=[\cos \,\,{{72}^{o}}-\cos \,{{36}^{o}}]\] \[=\left[ \frac{\sqrt{5}-1}{4}-\frac{\sqrt{5}+1}{4} \right]=\frac{-1}{2}\].
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