Embibe Experts Solutions for Exercise 5: Assignment

If ${cosec}^{-1}\left(2^x\right)+{\sec }^{-1}\left(x^2\right)=\frac{\pi }{2}$ then number of solutions of this equation is

If ${\left({\sin }^{-1}x\right)}^5+{\left({\sin }^{-1}y\right)}^5+{\left({\sin }^{-1}z\right)}^5=\frac{3{\pi }^5}{32}$ then the value of $5x^2+17y^2+19z^2+8xy+5yz+7zx$ is equal to

Number of solutions of $4{\cos }^{-1}\left(\cos \left|x\right|\right)=\left|x\right|$ is equal to

The value of ${\cot }^2\left({\cot }^{-1}3+{\cot }^{-1}7+{\cot }^{-1}13+{\cot }^{-1}21\right)$ is equal to

The value of ${\sin }^{-1}\left(\sin 9\right)+{\tan }^{-1}\left(\tan 9\right)$ is equal to

If $\alpha =3{\cos }^{-1}\left(\frac{5}{\sqrt{28}}\right)+3{\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$ and $\beta =4{\sin }^{-1}\left(\frac{7\sqrt{2}}{10}\right)-4{\tan }^{-1}\left(\frac{3}{4}\right)$ then value of $5\cos \alpha +10\sec \beta$ is equal to

The range of $f\left(x\right)={\cot }^{-1}\left(\frac{x^2}{1+x^2}\right)$ is $\left(a,b\right)$ then $\frac{3\pi }{a+b}$ is equal to

The number of positive integers in the domain of $f\left(x\right)={\cos }^{-1}\left(\left[e^x\right]-1\right)+{\sin }^{-1}\left(\left[e^x\right]\right)$, where $\left[·\right]$ represents greatest integer function, is equal to