Solve 20^circ*cos40^circ*cos60^circ*cos80^circ=1/16

$$20 ^ { \circ } \cdot \cos 40 ^ { \circ } \cdot \cos 60 ^ { \circ } \cdot \cos 80 ^ { \circ } = \frac { 1 } { 16 }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$20 \cdot 0.7733925716733684 = \frac{1}{16}$$

Multiply 20 and 0.7733925716733684 to get 15.467851433467368.

$$15.467851433467368=\frac{1}{16}$$

Convert decimal number 15.467851433467368 to fraction \frac{1933481429183421}{10000000000}. Reduce the fraction \frac{1933481429183421}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1933481429183421}{125000000000000}=\frac{1}{16}$$

Least common multiple of 125000000000000 and 16 is 125000000000000. Convert \frac{1933481429183421}{125000000000000} and \frac{1}{16} to fractions with denominator 125000000000000.

$$\frac{1933481429183421}{125000000000000}=\frac{7812500000000}{125000000000000}$$

Compare \frac{1933481429183421}{125000000000000} and \frac{7812500000000}{125000000000000}.

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