Question

The equation $3co{s}^{-1}x-\pi x-\frac{\pi }{2}=0$ has

• A. one negative solution
• B. one positive solution
• C. no solution
• D. more than one solution

Answer 1

Answer: (B)

one positive solution

Substituting $x=\frac{1}{2}$ , we get
$3co{s}^{-1}\left(\frac{1}{2}\right)-\frac{\pi }{2}-\frac{\pi }{2}$
$=3\left(\frac{\pi }{3}\right)-\pi$
$=0$
Hence there is one positive real solution to the above equation since range of $co{s}^{-1}\left(x\right)ϵ[\pi ,0]$.