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Q.
If the equation $\cos ^{-1} x+\cot ^{-1} x=\sin ^{-1}(\sin x)+2 p$ has atleast one solution then number of integral value(s) of $p$ is(are)
Inverse Trigonometric Functions
Solution:
$2 p=\cos ^{-1} x+\cot ^{-1} x-x \{\Theta-1 \leq x \leq 1\}$
$2 p \in\left[\frac{\pi}{4}-1, \frac{7 \pi}{4}+1\right]=[-0.72,6.4] $
$\Rightarrow p \in[-0.36,3.2]$
$\therefore \text { Number of integral values of } p \text { are } 4$