Mathematics - Trigonometric Equation Question with Solution | TestHub

$\frac{5}{4}{\cos }^{2}2\mathrm{x}+{\left({\sin }^2\mathrm{x}+{\cos }^2\mathrm{x}\right)}^2+{\left({\sin }^2\mathrm{x}+{\cos }^2\mathrm{x}\right)}^3-5{\sin }^2\mathrm{x}.{\cos }^2\mathrm{x}=2$
$\Rightarrow \frac{5}{4}\left(1-{\sin }^{2}2\mathrm{x}\right)-\frac{5}{4}{\sin }^{2}2\mathrm{x}+2=2$
$\Rightarrow 1-2{\sin }^{2}2\mathrm{x}=0$
$\Rightarrow {\sin }^{2}2\mathrm{x}=\frac{1}{2}\mathrm{ }$
$\Rightarrow 2\mathrm{x}=n\mathrm{\pi }\pm \frac{\mathrm{\pi }}{4}$
$\Rightarrow \mathrm{x}=\frac{\mathrm{n}\mathrm{\pi }}{2}\pm \frac{\mathrm{\pi }}{8}$
Number of solution = 8