A) \[\pi \]
B) \[\frac{5\pi }{4}\]
C) \[\frac{\pi }{2}\]
D) \[\frac{3\pi }{8}\]
Correct Answer: C
Solution :
| \[{{\sin }^{2}}2\theta +{{\cos }^{4}}2\theta =\frac{3}{4}\] |
| Let \[{{\cos }^{2}}2\theta =t\] |
| \[\Rightarrow \] \[1-{{\cos }^{2}}2\theta +{{\cos }^{4}}2\theta =\frac{3}{4}\] |
| \[\Rightarrow \] \[t=\frac{1}{2}\] \[\Rightarrow \] \[{{\cos }^{2}}2\theta =\frac{1}{2}\] |
| \[\Rightarrow \] \[2{{\cos }^{2}}2\theta -1=0\] |
| \[\Rightarrow \] \[\cos \,\,4\theta =0\] |
| \[\Rightarrow \] \[4\theta =(2n+1)\frac{\pi }{2}\] |
| \[\Rightarrow \] \[\theta =(2n+1)\frac{\pi }{8}\] |
| \[\Rightarrow \] \[\theta =\frac{\pi }{8},\frac{3\pi }{8}E\left[ 0,\frac{\pi }{2} \right]\] |
| Sum of value of \[\theta \] is \[\frac{\pi }{2}.\] |
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