Inverse Trigono...

Number of solution(s) to the equation$$ $$ $${\cos ^{ - 1}}x + {\sin ^{ - 1}}\left( {\dfrac{x}{2}} \right) = \dfrac{\pi }{6}\,$$ is/are 

$$\displaystyle \sum^{\infty}_{r=1}\tan^{-1}\left(\dfrac {3}{r^{2}-r+9}\right)$$ is -

$$If\,\cos \left( {2{{\sin }^{ - 1}}x} \right) = \frac{1}{9},\,then\,\,x\,\,is\,\,equal\,\,to$$

If $${ cos }^{ -1 }\dfrac { 3 }{ 5 } -{ sin }^{ -1 }\dfrac { 4 }{ 5 } ={ cos }^{ -1 }x$$, then x is equal to -

Number of solution of the equation $$\tan^{-1}\left(\dfrac {1}{x-1}+\dfrac {1}{x-2}+\dfrac {1}{x-3}+\dfrac {1}{x-4} \right)+\cos^{-1}(x)=\dfrac {3\pi}{4}-\sin^{-1}(x)$$ are

The range of the function $$f(x)=\ell n\ (\sin^{-1}(x^{2}+x))$$ is

If $$f(x)=\cos^{-1}\left(\dfrac {\sqrt {2x^{2}+1}}{x^{2}+1}\right)$$, then range of $$f(x)$$ is

$$cos^{-1}\left(\dfrac{\pi}{3}+sec^{-1}(-2)\right)$$=

The value of $$\cot\left(cosec^{-1}\dfrac{5}{3}+\tan^{-1}\dfrac{2}{3}\right)$$ is equal to-

$$\int _{ 0 }^{ \pi  }{ \left[ cotx \right] dx,where\left[ \cdot  \right]  } $$ denotes the greatest integer function, is equal to: