A) \[\tan \frac{\pi }{12}\]
B) \[\tan \frac{7\pi }{12}\]
C) \[\tan \frac{11\pi }{12}\]
D) \[\tan \frac{5\pi }{12}\]
Correct Answer: C
Solution :
\[f(x)=\sqrt{x},g(x)=tanx,\,h(x)=\frac{1-{{x}^{2}}}{1+{{x}^{2}}}\] \[fog(x)=\sqrt{\tan x}\] \[hofog(x)=h(\sqrt{\tan x})=\frac{1-\tan x}{1+\tan x}\] \[=-\tan \left( \frac{\pi }{4}-x \right)\] \[\phi (x)=\tan \left( \frac{\pi }{4}-x \right)\] \[\phi \left( \frac{\pi }{3} \right)=\tan \left( \frac{\pi }{4}-\frac{\pi }{3} \right)=\tan \left( -\frac{\pi }{12} \right)=-\tan \frac{\pi }{12}\] \[=\tan \left( \pi -\frac{\pi }{12} \right)=\tan \frac{11\pi }{12}\]
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