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

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

Evaluate

$$\frac{6498393924658126}{6180339887498949}\approx 1.051462224$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.3249196962329063}{0.30901699437494745}$$

Expand \frac{0.3249196962329063}{0.30901699437494745} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{32491969623290630}{30901699437494745}$$

Reduce the fraction \frac{32491969623290630}{30901699437494745} to lowest terms by extracting and canceling out 5.

$$\frac{6498393924658126}{6180339887498949}$$

Factor

$$\frac{2 \cdot 197 \cdot 670231 \cdot 24608509}{3 \cdot 17 \cdot 19 \cdot 2531 \cdot 5813 \cdot 433507} = 1\frac{318054037159177}{6180339887498949} = 1.051462224238267$$