Solve 1-tan15^circ/1+tan15^circ?

$$\frac { 1 - \tan 15 ^ { \circ } } { 1 + \tan 15 ^ { \circ } } ?$$

Evaluate

$$\frac{7320508075688773}{12679491924311227}\approx 0.577350269$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1 - 0.2679491924311227}{1 + 0.2679491924311227}$$

Subtract 0.2679491924311227 from 1 to get 0.7320508075688773.

$$\frac{0.7320508075688773}{1+0.2679491924311227}$$

Add 1 and 0.2679491924311227 to get 1.2679491924311227.

$$\frac{0.7320508075688773}{1.2679491924311227}$$

Expand \frac{0.7320508075688773}{1.2679491924311227} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{7320508075688773}{12679491924311227}$$

Factor

$$\frac{7 \cdot 67 \cdot 15608759223217}{23 \cdot 167 \cdot 3301091362747} = 0.5773502691896257$$