Question

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

Answer 1

$si{n}^4\frac{x}{2}-co{s}^4\frac{x}{2}=\frac{1}{4}$

$\Rightarrow (si{n}^2\frac{x}{2}-co{s}^2\frac{x}{2})(si{n}^2\frac{x}{2}+co{s}^2\frac{x}{2})=\frac{1}{4}$

$\Rightarrow si{n}^2\frac{x}{2}-co{s}^2\frac{x}{2}=\frac{1}{4}$

$\Rightarrow -cosx=\frac{1}{4}$

$\Rightarrow +cosx=-1/4$

$\therefore x=\pm co{s}^{-1}(-1/4)+2n\pi ;nϵ$ integers