Question

For the equation ${\cos }^{-1}x+{\cos }^{-1}2x+\pi =0$, the number of real solution is

• A. $1$
• B. $2$
• C. $0$
• D. infinity

Answer 1

The correct option is C

$0$

Finding the number of real solution:

${\cos }^{-1}x+{\cos }^{-1}2x+\mathrm{\pi }=0$

As, we know range of ${\cos }^{-1}xis\left[0,\mathrm{\pi }\right]$

$$\begin{gathered} {\cos }^{-1}x⩾0 \\ and{\cos }^{-1}2x⩾0 \end{gathered}$$

Sum of three positive number can not be zero

Therefore, there is no such $x$ exist.

Hence, option (C) is correct answer.