Question

The number of solutions of the equation $1+x^2+2xsin\left(co{s}^{-1}y\right)=0$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A)

1

$1+x^2+2xsinco{s}^{1-}y=0$
$\Rightarrow 1+x^2+2x\sqrt{1-y^2}=0$
$x^2+2x\sqrt{1-y^2}+1=0$
$x^2+2x\sqrt{1-y^2}+1-y^2=-y^2$
$(x+\sqrt{1-y^2})=-y^2\Rightarrow -y^2\ge 0$
$x+\sqrt{1-y^2}=0andy=0(x+\sqrt{1-y^2}{)}^2\ge 0$
$\to y=0,x=-1$ only one solution