\cos x\cos2x\cos3x=\frac{1}{4}\cos2x|\div\cos2x\\
\cos x\cdot\cos3x=\frac{1}{4};\\
\cos x\cos(x+2x)=\frac{1}{4};\\
\cos x(\cos x\cos2x-\sin x\sin2x)=\frac{1}{4};\\
\cos x(\cos x\cos2x-2\sin x\sin x\cos x)=\frac{1}{4};\\
\cos^2x(\cos2x-2\sin^2x)=\frac{1}{4};\\" alt="\cos x\cdot\cos2x\cdot\cos3x=0,25\cdot\cos2x;\\
a) \cos2x=0;\ \ 2x=\frac{\pi}{2}+\pi n, n\in Z\\
x=\frac{\pi}{4}+\frac{\pi n}{2}, n\in Z\\
b)\cos2x\neq0==>\cos x\cos2x\cos3x=\frac{1}{4}\cos2x|\div\cos2x\\
\cos x\cdot\cos3x=\frac{1}{4};\\
\cos x\cos(x+2x)=\frac{1}{4};\\
\cos x(\cos x\cos2x-\sin x\sin2x)=\frac{1}{4};\\
\cos x(\cos x\cos2x-2\sin x\sin x\cos x)=\frac{1}{4};\\
\cos^2x(\cos2x-2\sin^2x)=\frac{1}{4};\\" align="absmiddle" class="latex-formula">
2(2t^2-t+2t-1)=1;\\
4t^2+2t-3=0;\\
D=b^2-4ac=2^2-4\cdot4\cdot(-3)=4+48=52=(4\sqrt{13})^2;\\
t_1=\frac{-b-\sqrt D}{2a}=\frac{-2-4\sqrt{13}}{8}\notin[-1;1];\\" alt="\cos^2x(2\cos^2x-1-2\sin^2x)=\frac{1}{4};\\
\cos^2x(2(\cos^2x-\sin^2x)-1))=\frac{1}{4};\\
\cos^2x(2\cos2x-1)=\frac{1}{4};\\
2\cos^2x(2\cos2x-1)=\frac{1}{2};\\
(2\cos^2x-1+1)(2\cos2x-1)=\frac{1}{2};\\
2(\cos2x+1)(2\cos2x-1)=1;\\
\cos2x=t;\ \ -1\leq t\leq1;\\
2(t+1)(2t-1)=1;==>2(2t^2-t+2t-1)=1;\\
4t^2+2t-3=0;\\
D=b^2-4ac=2^2-4\cdot4\cdot(-3)=4+48=52=(4\sqrt{13})^2;\\
t_1=\frac{-b-\sqrt D}{2a}=\frac{-2-4\sqrt{13}}{8}\notin[-1;1];\\" align="absmiddle" class="latex-formula">
ответ: