Solve cos20^circ*cos40^circ*cos80^circ=1/8

$$\cos 20 ^ { \circ } \cdot \cos 40 ^ { \circ } \cdot \cos 80 ^ { \circ } = \frac { 1 } { 8 }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$0.9405657543138218 = \frac{1}{8}$$

Convert decimal number 0.9405657543138218 to fraction \frac{4702828771569109}{10000000000}. Reduce the fraction \frac{4702828771569109}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{4702828771569109}{5000000000000000}=\frac{1}{8}$$

Least common multiple of 5000000000000000 and 8 is 5000000000000000. Convert \frac{4702828771569109}{5000000000000000} and \frac{1}{8} to fractions with denominator 5000000000000000.

$$\frac{4702828771569109}{5000000000000000}=\frac{625000000000000}{5000000000000000}$$

Compare \frac{4702828771569109}{5000000000000000} and \frac{625000000000000}{5000000000000000}.

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