Solve tan37^circ+tan23^circ/1-tan37^circtan23^circ

$$\frac { \tan 37 ^ { \circ } + \tan 23 ^ { \circ } } { 1 - \tan 37 ^ { \circ } \tan 23 ^ { \circ } }$$

Evaluate

$$\frac{58901443315619945000000000000000}{34006764153930659013177582627363}\approx 1.732050808$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.7535540501027942 + 0.4244748162096047}{1 - 0.7535540501027942 \cdot 0.4244748162096047}$$

Add 0.7535540501027942 and 0.4244748162096047 to get 1.1780288663123989.

$$\frac{1.1780288663123989}{1-0.7535540501027942\times 0.4244748162096047}$$

Multiply 0.7535540501027942 and 0.4244748162096047 to get 0.31986471692138681973644834745274.

$$\frac{1.1780288663123989}{1-0.31986471692138681973644834745274}$$

Subtract 0.31986471692138681973644834745274 from 1 to get 0.68013528307861318026355165254726.

$$\frac{1.1780288663123989}{0.68013528307861318026355165254726}$$

Expand \frac{1.1780288663123989}{0.68013528307861318026355165254726} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$\frac{117802886631239890000000000000000}{68013528307861318026355165254726}$$

Reduce the fraction \frac{117802886631239890000000000000000}{68013528307861318026355165254726} to lowest terms by extracting and canceling out 2.

$$\frac{58901443315619945000000000000000}{34006764153930659013177582627363}$$