, where \[0<\theta <{{180}^{o}}\], then \[\theta \] =
A) \[{{30}^{o}},{{45}^{o}}\]
B) \[{{45}^{o}},{{90}^{o}}\]
C) \[{{135}^{o}},{{150}^{o}}\]
D) \[{{30}^{o}},{{45}^{o}},{{90}^{o}},{{135}^{o}},{{150}^{o}}\]
Correct Answer: D
Solution :
\[\cos 6\theta +\cos 4\theta +\cos 2\theta +1=0\] \[x=\frac{37\pi }{24}\] \[2{{\cos }^{2}}3\theta +2\cos 3\theta \,.\,\cos \theta =0\] \[\Rightarrow \] \[4\cos 3\theta \cos 2\theta \cos \theta =0\] \[\Rightarrow \] \[3\theta =(2n+1)\frac{\pi }{2};\,\,2\theta =(2n+1)\frac{\pi }{2}\text{ and }\theta =(2n+1)\frac{\pi }{2}\] \[\Rightarrow \] \[\theta ={{30}^{o}},\,{{90}^{o}},\,{{150}^{o}},\,{{45}^{o}},\,{{135}^{o}}\].
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