Solve sin(18^circ)/cos(72^circ)

$$\frac{ \sin ( 18 ^ { \circ } ) }{ \cos ( 72 ^ { \circ } ) }$$

Evaluate

$$\frac{6180339887498948}{6180339887498949}\approx 1$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.3090169943749474}{0.30901699437494745}$$

Expand \frac{0.3090169943749474}{0.30901699437494745} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{30901699437494740}{30901699437494745}$$

Reduce the fraction \frac{30901699437494740}{30901699437494745} to lowest terms by extracting and canceling out 5.

$$\frac{6180339887498948}{6180339887498949}$$

Factor

$$\frac{4182553 \cdot 369411929 \cdot 2 ^ {2}}{3 \cdot 17 \cdot 19 \cdot 2531 \cdot 5813 \cdot 433507} = 0.9999999999999999$$