Question

If the equation ${\cos }^{-1}x+{\cot }^{-1}x={\sin }^{-1}(\sin x)+2p$ has atleast one solution then number of integral value(s) of $p$ is(are)

• A. 3
• B. 4
• C. 6
• D. 7

Answer 1

Answer: (B)

$2p={\cos }^{-1}x+{\cot }^{-1}x-x\{\Theta -1\le x\le 1\}$
$2p\in \left[\frac{\pi }{4}-1,\frac{7\pi }{4}+1\right]=[-0.72,6.4]$
$\Rightarrow p\in [-0.36,3.2]$
$\therefore \text{ Number of integral values of }p\text{ are }4$