Question

Solve the following equations.
$co{s}^4\frac{x}{5}+si{n}^2\frac{x}{5}=1.$

Answer 1

${\cos }^4\frac{x}{5}+{\sin }^2\frac{x}{5}=1={\cos }^2\frac{x}{5}+{\sin }^2\frac{x}{5}$

$\Rightarrow {\cos }^4\frac{x}{5}={\cos }^2\frac{x}{5}$

$\Rightarrow {\cos }^2\frac{x}{5}(\cos \frac{x}{5}-1)(\cos \frac{x}{5}+1)=0$

${\cos }^2\frac{x}{5}=0,\frac{x}{5}=\frac{(2n+1)\pi }{2},x=\frac{5(2n+1)\pi }{2}$

Or

$\cos \frac{x}{5}=1,\frac{x}{5}=2n\pi ,x=10n\pi$

Or

$\cos \frac{x}{5}=-1,\frac{x}{5}=(2n+1)\pi ,x=5(2n+1)\pi$