Inverse Trigono...

If $${ sin }^{ -1 }\left( a-\frac { { a }^{ 2 } }{ 3 } +\frac { { a }^{ 3 } }{ 9 } -...........\infty  \right) +{ cos }^{ -1 }\left( 1+b+{ b }^{ 2 }+.......\infty  \right) =\frac { \pi  }{ 2 } $$

If $$(cot^{-1}x)^{2}-3(cot^{-1}x)+2 > 0,$$ then x lies in

The solution of the equation $$sin^{-1}(\frac{dt}{dx})=x+y$$ is

Thee value of $$\cos^{-1}x+\cos^{-1}\left(\dfrac {x}{2}+\dfrac {\sqrt {3-x^{2}}}{2}\right)$$, where $$\dfrac {1}{2} \le x \le 1$$.

The value of $${ tan }^{ -1 }\left( \frac { xcos\theta  }{ 1-xsin\theta  }  \right) -{ cot }^{ -1 }\left( \frac { cos\theta  }{ x-sin\theta  }  \right) $$ is :

If $${ sin }^{ -1 }\left( \frac { x }{ 5 } \right) +{ cosec }^{ -1 }\left( \frac { 5 }{ 4 } \right) =\frac { \pi }{ 2 } $$, then value of x is :

Let $$S_{n}=\cot^{-1}\left(3x+\dfrac{2}{x}\right)+ \cot^{-1}\left(6x+\dfrac{2}{x}\right)+ \cot^{-1}\left(10x+\dfrac{2}{x}\right)+.....+n$$ term where $$x>0$$. If $$\displaystyle \lim_{n\rightarrow \infty}S_{n}=$$ then $$x$$ equals

The number of solution of the equation $${\sin ^{ - 1}}\left( {1 - x} \right) - 2{\sin ^{ - 1}}x = \frac{\pi }{2}$$ is are 

Let f:-$$\left\{ 0,4\pi  \right\} $$$$\rightarrow \left[ 0,\pi  \right] $$ be defined by f(x)=$${ cos }^{ -1 }\left( cosx \right) $$. The number of points x$$\in \left[ 0,4\pi  \right] $$ satisfying the equation f(x)=$$\frac { 10-x }{ 10 } $$ is

$$cos^{-1}[cos(-\frac{17}{15}\pi )]$$ is equal to-