Mathematics - Trigonometric Equation Question with Solution | TestHub

Given, $\sin x={\cos }^{2}x$

$\Rightarrow \sin x=1-{\sin }^{2}x$

$\Rightarrow {\sin }^{2}x+\sin x-1=0$

$\Rightarrow \sin x=\frac{\left(-1\pm \sqrt{5}\right)}{2}$

$\Rightarrow \sin x=\frac{\left(\sqrt{5}-1\right)}{2}$

Now plotting the graph we get,

$\Rightarrow$Now by graph number of solutions in $\left(0,10\right)=4$