Question

The number of real solutions of ${\cos }^{-1}x+{\cos }^{-1}2x=-\pi$ is

• A. $0$
• B. $1$
• C. $2$
• D. None

Answer 1

The correct option is A $0$

${\cos }^{-1}x+{\cos }^{-1}2x=-\pi$

We know that, range of ${\cos }^{-1}x$ is $[0,\pi ]$ and range of ${\cos }^{-1}2x$ is $[0,\pi ]$.

So, here we can see both ranges are in positive quantity.

So, sum of positive quantity cannot be negative quantity.

$\therefore$ ${\cos }^{-1}x+{\cos }^{-1}2x=-\pi$ is not possible.

$\therefore$ The number of real solution is $0.$