A) \[\frac{5\pi }{4}\]
B) \[\frac{\pi }{2}\]
C) \[\pi \]
D) \[\frac{3\,\pi }{8}\]
Correct Answer: B
Solution :
\[1-co{{s}^{2}}2\theta +co{{s}^{4}}2\theta =\frac{3}{4}\] \[\Rightarrow \,\,co{{s}^{4}}2\theta -co{{s}^{2}}2\theta +\frac{1}{4}=\,\,0\] \[\Rightarrow \,\,{{\left( co{{s}^{2}}2\theta -\frac{1}{2} \right)}^{2}}=\,0\] \[co{{s}^{2}}2\theta =\frac{1}{2}={{\cos }^{2}}\frac{\pi }{4}\text{ }\] \[2\theta =n\pi +\frac{\pi }{4}\] \[\theta \,=\,\frac{n\pi }{2}+\frac{\pi }{8}\,\,\,\,\,\,\,\,\,\,\,\theta \in \,\,\left( 0,\frac{\pi }{2} \right)\] \[n=0\,\,\,\,\,\,\theta \,\,=\,\,\frac{\pi }{8}\] \[n=1\,\,\,\,\,\theta =\frac{\pi }{2}+\frac{\pi }{8}=\frac{5\pi }{8}\] \[\theta =\frac{\pi }{2}-\frac{\pi }{8}=\frac{3\pi }{8}\] Sum of angles \[=\frac{\pi }{8}+\frac{3\pi }{8}=\frac{\pi }{2}\]
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