Solve tan50^circ-tan40/2tan10^circ

$$\frac { \tan 50 ^ { \circ } - \tan 40 } { 2 \tan 10 ^ { \circ } }$$

Evaluate

$$\frac{17632698070846505}{17632698070846498}\approx 1$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1.19175359259421 - 0.8390996311772799}{2 \cdot 0.17632698070846498}$$

Subtract 0.8390996311772799 from 1.19175359259421 to get 0.3526539614169301.

$$\frac{0.3526539614169301}{2\times 0.17632698070846498}$$

Multiply 2 and 0.17632698070846498 to get 0.35265396141692996.

$$\frac{0.3526539614169301}{0.35265396141692996}$$

Expand \frac{0.3526539614169301}{0.35265396141692996} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{35265396141693010}{35265396141692996}$$

Reduce the fraction \frac{35265396141693010}{35265396141692996} to lowest terms by extracting and canceling out 2.

$$\frac{17632698070846505}{17632698070846498}$$

Factor

$$\frac{5 \cdot 47 \cdot 75032757748283}{2 \cdot 53 \cdot 233 \cdot 48481 \cdot 14726021} = 1\frac{6}{17632698070846498} = 1.0000000000000004$$