K. C. Sinha Solutions for Chapter: Inverse Circular Functions, Exercise 1: EXERCISE

The value of ${\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)+{\sin }^{-1}\left(\frac{1}{\sqrt{2}}\right)$ is equal to

The set of values of $x$ for which the formula $2{\sin }^{-1}x={\sin }^{-1}\left(2x\sqrt{1-x^2}\right)$ is true, is

If ${\cot }^{-1}\left(\frac{n}{\pi }\right)>\frac{\pi }{6},n$ being a natural number, then maximum value of $n$ is

If we consider only the principal values of the inverse trigonometric functions, then the value of $\tan \left({\cos }^{-1}\frac{1}{\sqrt{2}}-{\sin }^{-1}\frac{4}{\sqrt{17}}\right)$ is

If $\sum _{i=1}^{10}{\sin }^{-1}{x}_i=5\pi$, then $\sum _{i=1}^{10}{x}_i^2=$

If $x=\sin \left(2{\tan }^{-1}2\right)$ and $y=\sin \left(\frac{1}{2}{\tan }^{-1}\frac{4}{3}\right)$, then

The set of values of $a$ for which $x^2+ax+{\sin }^{-1}\left(x^2-4x+5\right)+{\cos }^{-1}\left(x^2-4x+5\right)=0$ has at least one solution is

If ${\tan }^{-1}\left(x+h\right)={\tan }^{-1}\left(x\right)+\left(h \sin y\right)\left(\sin y\right)-{\left(h\sin y\right)}^2·\frac{{\sin }^{2}y}{2}+{\left(h\sin y\right)}^3·\frac{{\sin }^{3}y}{3}+\dots$ where $x\in \left(0,1\right),y\in \left(\frac{\pi }{4},\frac{\pi }{2}\right)$, then