If \({x}{\sin{{a}}}+{y}{\sin{{2}}}{a}+{z}{\sin{{3}}}{a}={\sin{{4}}}{a}\)
\({x}{\sin{{b}}}+{y}{\sin{{2}}}{b}+{z}{\sin{{3}}}{b}={\sin{{4}}}{b}\),
\({x}{\sin{{c}}}+{y}{\sin{{2}}}{c}+{z}{\sin{{3}}}{c}={\sin{{4}}}{c}\),
then the roots of the equation \({t}^{{3}}-{\left(\frac{{z}}{{2}}\right)}{t}^{{2}}-{\left(\frac{{{y}+{2}}}{{4}}\right)}{t}+{\left(\frac{{{z}-{x}}}{{8}}\right)}={0},{a},{b},{c},\ne{n}\pi,\)
are
(a)\({\sin{{a}}},{\sin{{b}}},{\sin{{c}}}\)
(b) \({\cos{{a}}},{\cos{{b}}},{\cos{{c}}}\)
(b)\({\sin{{2}}}{a},{\sin{{2}}}{b},{\sin{{2}}}{c}\)
(d) \({\cos{{2}}}{a},{\cos{{2}}}{b}{\cos{{2}}}{c}\)