Single Choice

If $$\cos ^{ -1 }{ x } -\sin ^{ -1 }{ x } =0$$, then $$x$$ is equal to-

A$$\pm \cfrac { 1 }{ \sqrt { 2 } } $$
B$$1$$
C$$\pm \cfrac { 1 }{ \sqrt { 3 } } $$
D$$\cfrac{1}{\sqrt {2}}$$
Correct Answer

Solution

We know, $$\displaystyle \cos ^{ -1 }{ \theta } +\sin ^{ -1 }{ \theta } =\frac { \pi }{ 2 } $$ $$\therefore \cos ^{ -1 }{ x } -\sin ^{ -1 }{ x } =0$$ $$\displaystyle \Rightarrow \cos ^{ -1 }{ x } -\frac { \pi }{ 2 } +\cos ^{ -1 }{ x } =0$$ $$\displaystyle \Rightarrow 2\cos ^{ -1 }{ x } =\frac { \pi }{ 2 } \Rightarrow \cos ^{ -1 }{ x } =\frac { \pi }{ 4 } $$ $$\displaystyle \Rightarrow x=\frac { 1 }{ \sqrt { 2 } } $$

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