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If $$\displaystyle \:\sum_{i= 1}^{10}\cos^{-1}x_{i}= 0$$, then $$\displaystyle \:\sum_{i= 1}^{10}x_{i}$$  is

If $$\displaystyle \:\sum_{i= 1}^{2n}\sin^{-1}x_{i}= n\pi$$, then $$\displaystyle \:\sum_{i= 1}^{2n}x_{i}$$  is equal to

If both $$\displaystyle \:\alpha, \beta $$ and $$\displaystyle \:6x^{2}+11x+3= 0$$ are real roots of the equation then

The range of the the function, $$f(x)=(\cot ^{-1}x+\sec ^{-1}x+cosec ^{-1}x)$$ is

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

If $$\displaystyle \:\cos ^{-1}\lambda +\cos^{-1}\mu +\cos ^{-1}v= 3\pi $$ then $$\lambda \mu +\mu v+v\lambda $$ is equal to

If $$A=\cot ^{ -1 }{ \sqrt { \tan { \theta  }  }  } -\tan ^{ -1 }{ \sqrt { \tan { \theta  }  }  }$$, then $$\displaystyle \tan { \left( \frac { \pi  }{ 4 } -\frac { A }{ 2 }  \right)  } $$ is equal to 

The principal value of $$\displaystyle \:\sin ^{-1}\left \{ \cos \left ( \sin ^{-1}\dfrac{\sqrt{3}}{2} \right ) \right \}$$ is

A function $$f(x)=\sqrt{1-2x}+x$$ is defined from $$D_{1}\rightarrow D_{2}$$ and is onto. If the set $$D_{1}$$ is its complete domain then the set $$D_{2}$$ is

The set of values of $$x$$ for which $$\displaystyle \:\tan ^{-1}\frac{x}{\sqrt{1-x^{2}}}= \sin ^{-1}x$$ holds is