A) 0
B) \[\frac{1}{\sqrt{10}}\]
C) \[\frac{2}{\sqrt{10}}\]
D) \[\frac{-2}{\sqrt{10}}\]
Correct Answer: B
Solution :
\[\alpha =\beta \] \[\therefore \,\,\sin \,\alpha \,=\sin \,\beta \] \[\Rightarrow \,\sqrt{1-{{x}^{2}}}=3x\] \[\Rightarrow \,1-{{x}^{2}}=9{{x}^{2}}\,\Rightarrow \,10{{x}^{2}}-1\] \[\Rightarrow \,x=\frac{1}{\sqrt{10}}\,\,,\,\frac{-1}{\sqrt{10}}\] \[\therefore \,\,x=\frac{1}{\sqrt{10}}\]
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