Question

If $6si{n}^{-1}(x^2-6x+8.5)=\pi$ , then the number of solutions of $x$ is

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is B $2$

Given $6si{n}^{-1}(x^2-6x+8.5)=\pi$
$si{n}^{-1}(x^2-6x+8.5)=\frac{\pi }{6}$
Take $sin$ both sides.
$sinsi{n}^{-1}(x^2-6x+8.5)=sin\frac{\pi }{6}=\frac{1}{2}$
$x^2-6x+8.5=0.5[\because sinsi{n}^{-1}x=x]$
$x^2-6x+8=0$
$x=\frac{6\pm \sqrt{36-32}}{2}=\frac{6\pm 2}{2}$
$\Rightarrow x=4$ or $2$
Hence, there are two solutions.