A) \[\frac{1}{\sqrt{3}}\]
B) \[\frac{2}{\sqrt{3}}\]
C) \[\sqrt{3}\]
D) \[1\]
Correct Answer: A
Solution :
| [a] Given,\[\tan (x+y)\tan (x-y)=1\] \[\Rightarrow \] \[\tan \,(x+y)=\cot (x-y)\] \[\Rightarrow \] \[\tan \,(x+y)=\tan \,[90{}^\circ -(x-y)]\] \[\Rightarrow \] \[=h\,m\] \[\Rightarrow \] \[2x=90{}^\circ \] \[\therefore \] \[x=\frac{90{}^\circ }{2}=45{}^\circ \] \[\therefore \] \[\tan \left( \frac{2x}{3} \right)=\tan \left( \frac{2\times 45{}^\circ }{3} \right)\] \[=\tan 30{}^\circ =\frac{1}{\sqrt{3}}\] |
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