A) \[{{90}^{o}},{{60}^{o}},{{30}^{o}}\]
B) \[{{90}^{o}},{{150}^{o}},{{60}^{o}}\]
C) \[{{90}^{o}},{{45}^{o}},{{150}^{o}}\]
D) \[{{90}^{o}},{{30}^{o}},{{150}^{o}}\]
Correct Answer: D
Solution :
\[\sin 2\theta =\cos \theta \Rightarrow \cos \theta =\cos \left( \frac{\pi }{2}-2\theta \right)\] \[\Rightarrow \] \[\theta =2n\pi \pm \left( \frac{\pi }{2}-2\theta \right)\Rightarrow \theta \pm 2\theta =2n\pi \pm \frac{\pi }{2}\] i.e., \[3\theta =2n\pi +\frac{\pi }{2}\Rightarrow \theta =\frac{1}{3}\left( 2n\pi +\frac{\pi }{2} \right)\] and \[-\theta =2n\pi -\frac{\pi }{2}\Rightarrow \theta =-\left( 2n\pi -\frac{\pi }{2} \right)\] Hence value of \[\theta \] between 0 and \[\pi \] are \[\frac{\pi }{6},\,\frac{\pi }{2},\,\frac{5\pi }{6}\] i.e., \[{{30}^{o}},\,{{90}^{o}},\,{{150}^{o}}\].
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