Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

Let $a={\cos }^{-1}x,b={\sin }^{-1}y$

$a^2+b=1\&a+b^2=1\Rightarrow a=b$ or $a=1,b=o$ or $a=1,b=0$ If $a^{2}b\Rightarrow a^2+a-10\Rightarrow a=\frac{-1\pm \sqrt{5}}{2}$

$\begin{array}{rlrl}& a\in (o,\pi )b\in \left(\frac{-\pi }{2},\frac{\pi }{2}\right)& & \end{array}$

$\Rightarrow a=b=\frac{\sqrt{5}-1}{2}\Rightarrow (x,y)=\left({\cos }^{-1}\left(\frac{\sqrt{5}-1}{2}\right),\right)$

${\sin }^{-1}\left(\frac{\sqrt{5}-1}{2}\right)a=1,b=0\Rightarrow (x,y)=$

$\left({\cos }^1,0\right)a=0,b=1\Rightarrow (x,y)=(1,\sin 1)$