A) \[\frac{4}{17}\]
B) \[\frac{3}{17}\]
C) \[\frac{16}{17}\]
D) \[\frac{5}{17}\]
Correct Answer: C
Solution :
\[{{\tan }^{2}}\theta -4=3\tan \theta \] \[{{\tan }^{2}}\theta -3\tan \theta -4=0\] \[{{\tan }^{2}}\theta -4\tan \theta +\tan \theta -4=0\] \[\tan \theta \left( \tan \theta -4 \right)+1\left( \tan \theta -4 \right)=0\] \[\left( \tan \theta +1 \right)\left( \tan \theta -4 \right)=0\] \[\tan \,\theta =-1\] [Not Applicable] \[\tan \theta =4\] \[\left[ \because \,\sin \theta =\frac{\tan \theta }{\sqrt{1+{{\tan }^{2}}\theta }} \right]\] \[\sin \theta =\frac{4}{17}\Rightarrow \,{{\sin }^{2}}\theta =\frac{16}{17}\]
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