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[possward]

(a/sin(x) + b/cos(x))' = 0
-a*cos(x)/(sin(x)^2) + b*sin(x)/(cos(x)^2) = 0
(b*(sin(x)^3) - a*(cos(x)^3))/((sin(x)^2)*(cos(x)^2)) = 0
b*(sin(x)^3) - a*(cos(x)^3) = 0
(sin(x)^3)/(cos(x)^3) = a/b
tg(x)^3 = a/b
x = arctg(корень третьей степени из a/b)