A) 0
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{6}\]
D) \[\frac{\pi }{2}\]
Correct Answer: A
Solution :
[a] We have \[{{\sin }^{-1}}\left\{ \cot \left( {{\sin }^{-1}}\sqrt{\left( \frac{2-\sqrt{3}}{4} \right)}+{{\cos }^{-1}}\frac{\sqrt{12}}{4}+{{\sec }^{-1}}\sqrt{2} \right) \right\}\]\[={{\sin }^{-1}}\left\{ \cot \left( {{\sin }^{-1}}\sqrt{{{\left( \frac{\sqrt{3}-1}{2\sqrt{2}} \right)}^{2}}}+{{\cos }^{-1}}\frac{\sqrt{3}}{2}+{{\cos }^{-1}}\frac{1}{\sqrt{2}} \right) \right\}\]\[={{\sin }^{-1}}\{cot(15{}^\circ +30{}^\circ +45{}^\circ )\}=si{{n}^{-1}}(cot90{}^\circ )\] \[={{\sin }^{-1}}0=0\]
You need to login to perform this action.
You will be redirected in
3 sec
