Use half angle formulas to fill in the blanks in the identity below:


$\displaystyle {\left({\sin{{\left({5}{x}\right)}}}\right)}^{{4}}$ = $\displaystyle -{\frac{{{1}}}{{{2}}}}{\cos{{(}}}$ $\displaystyle {x}$ )$\displaystyle +{\frac{{{1}}}{{{8}}}}{\cos{{(}}}$ $\displaystyle {x}$)