Question

If value of x which satisfy equation ${\cos }^{-1}x<2$ is $xϵ(a,b]$.
Find the value of $a+b$.

• A. $-1-\cos 2$
• B. $1-\cos 2$
• C. $-1+\cos 2$
• D. $1+\cos 2$

Answer 1

The correct option is D $1+\cos 2$

Given, ${\cos }^{-1}x<2$
Also we know that, $0\le {\cos }^{-1}x\le \pi$
or $0\le {\cos }^{-1}x<2$
or $\cos 0\ge x>\cos 2$ ($\because {\cos }^{-1}x$is decreasing function)
$\Rightarrow$ $xϵ(\cos 2,1]$