Inverse Trigono...

The value of $$sin^{-1}(sin2010^{0})+cos^{-1}(cos2010^{0})+tan^{-1}(tan2010^{0})$$ is

The number of solutions of the equation $$1+x^{2}+2x\, sin\: (cos^{-1}y)=0$$ is 

The value of $$\displaystyle \sec^{-1}\left (\displaystyle \frac{1}{1-2x^{2}}\right)+4{\cos^{-1}}\sqrt{\displaystyle \frac{1+x}{2}}$$ is equal to

The value of $$\sin^{-1}$$$$\left \{ \tan\left ( \cos^{-1}\sqrt{\dfrac{2+\sqrt{3}}{4}}+\cos^{-1}\dfrac{\sqrt{12}}{4} -\text{cosec}^{-1}\sqrt{2}\right ) \right \}$$, is

If $$x> 0\, $$ and $$\, cos^{-1}\left ( \dfrac{12}{x} \right )+cos^{-1}\left ( \dfrac{35}{x} \right )=\dfrac{\pi }{2},$$ then x is

If $$cosec ^{ -1 }\left(cosec (x) \right)$$ and $$cosec\left(cosec ^{ -1 }(x) \right) $$ are equal functions, then the maximum range of value of $$x$$ is

The range of values of p for which the equation $$\sin \cos ^{-1}(\cos (\tan ^{-1}x))= p$$ has a solution is

The solution set of the equation $$\displaystyle \sin^{-1} \sqrt{1-x} + \cos^{-1}x = \cot^{-1} \left ( \frac{\sqrt{1-x^{2}}}{x} \right )-\sin^{-1}x$$

If $$\sin ^{ -1 }{ x } +\sin ^{ -1 }{ y } +\sin ^{ -1 }{ z } =\cfrac { 3\pi  }{ 2 } $$ and $$f(1)=2,f(x+y)=f(x)f(y)$$  for all  $$x,y\in R$$. Then $${ x }^{ { f(1) } }+{ y }^{ f(2) }+{ z }^{ f(3) }-\cfrac { x+y+z }{ { x }^{ f(1) }+{ y }^{ f(2) }+{ z }^{ f(3) } } $$ is equal to

If $$\left[ \sin ^{ -1 }{ \cos ^{ -1 }{ \sin ^{ -1 }{ \tan ^{ -1 }{ \theta  }  }  }  }  \right] =1$$, where $$[.]$$ denotes the greatest integer function, the $$\theta$$ lies in the interval