Solve cos(20)+sin(20)/cos(20)-sin(20)

$$\frac{ \cos ( 20 ) + \sin ( 20 ) }{ \cos ( 20 ) - \sin ( 20 ) }$$

Evaluate

$$\frac{12817127641115771}{5976724774602397}\approx 2.144506921$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.9396926207859084 + 0.3420201433256687}{0.9396926207859084 - 0.3420201433256687}$$

Add 0.9396926207859084 and 0.3420201433256687 to get 1.2817127641115771.

$$\frac{1.2817127641115771}{0.9396926207859084-0.3420201433256687}$$

Subtract 0.3420201433256687 from 0.9396926207859084 to get 0.5976724774602397.

$$\frac{1.2817127641115771}{0.5976724774602397}$$

Expand \frac{1.2817127641115771}{0.5976724774602397} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{12817127641115771}{5976724774602397}$$

Factor

$$\frac{12817127641115771}{37 \cdot 1381 \cdot 116968212901} = 2\frac{863678091910978}{5976724774602397} = 2.1445069205095586$$