A) One
B) Two
C) Four
D) Infinite
Correct Answer: B
Solution :
[b] As given : \[\cos \left( {{\sin }^{-1}}x \right)=\frac{1}{2}\] \[\Rightarrow {{\sin }^{-1}}x={{\cos }^{-1}}\left( \frac{1}{2} \right)\] \[\Rightarrow x=\sin \frac{\pi }{3}=\frac{\sqrt{3}}{2}\] \[\therefore \tan (co{{s}^{-1}}x)=tan\left( {{\cos }^{-1}}\frac{\sqrt{3}}{2} \right)\] \[=\tan \left( \pm \frac{\pi }{6} \right)=\pm \frac{1}{\sqrt{3}}\] Hence, \[\tan (co{{s}^{-1}}x)\] have two values.
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