Question #17956

cos20 degre*cos40*cos60*

Expert's answer

Conditions

cos20 degre*cos40*cos60*

Solution

cos20cos40cos60=cos(4020)+cos(40+20)2cos60=cos20+12212=cos204+180.355923155\begin{array}{l} \cos 20{}^\circ \cos 40{}^\circ \cos 60{}^\circ = \frac{\cos(40{}^\circ - 20{}^\circ) + \cos(40{}^\circ + 20{}^\circ)}{2} \cos 60{}^\circ = \frac{\cos 20{}^\circ + \frac{1}{2}}{2} \cdot \frac{1}{2} = \frac{\cos 20{}^\circ}{4} + \frac{1}{8} \\ \approx 0.355923155 \end{array}

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