Solve cos144^circ+cos216^circ/tan306^circ*cos306^circ

$$\frac { \cos 144 ^ { \circ } + \cos 216 ^ { \circ } } { \tan 306 ^ { \circ } \cdot \cos 306 ^ { \circ } }$$

Evaluate

$$\frac{647213595499957920}{961418553783773}\approx 673.186088362$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{-0.8090169943749473 + -0.8090169943749475}{-0.0024035463844594325}$$

Subtract 0.8090169943749475 from -0.8090169943749473 to get -1.6180339887498948.

$$\frac{-1.6180339887498948}{-0.0024035463844594325}$$

Expand \frac{-1.6180339887498948}{-0.0024035463844594325} by multiplying both numerator and the denominator by 10000000000000000000.

$$\frac{-16180339887498948000}{-24035463844594325}$$

Reduce the fraction \frac{-16180339887498948000}{-24035463844594325} to lowest terms by extracting and canceling out -25.

$$\frac{647213595499957920}{961418553783773}$$

Factor

$$\frac{3 \cdot 5 \cdot 7 \cdot 17 \cdot 11330770229341 \cdot 2 ^ {5}}{23 \cdot 79 \cdot 311 \cdot 1701363779} = 673\frac{178908803478659}{961418553783773} = 673.186088361593$$