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Решите задачу:

$cos10\cdot cos30\cdot cos50\cdot cos70 = \\ =\frac{\sqrt{3}}{2}\cdot\frac{1}{2}(cos(50-10)+cos(50+10))\cdot cos(90-20)= \\ = \frac{\sqrt{3}}{4}(cos40+cos60)\cdot sin20= \\ =\frac{\sqrt{3}}{4}(cos40\cdot sin20+\frac{1}{2}\cdot sin20)= \\ =\frac{\sqrt{3}}{4}(\frac{1}{2}(sin(20-40)+sin(20+40)+\frac{1}{2}sin20)= \\ =\frac{\sqrt{3}}{4}(\frac{1}{2}(-sin20+sin60)+\frac{1}{2}sin20)= \\ =\frac{\sqrt{3}}{4}(-\frac{1}{2}sin20+\frac{\sqrt{3}}{4}+\frac{1}{2}sin20)=\frac{3}{16}$