Solve tan10^circ+1/tan10^circ

$$\tan 10 ^ { \circ } + \frac { 1 } { \tan 10 ^ { \circ } }$$

Evaluate

$$\frac{2577728010314408453050608569716001}{440817451771162450000000000000000}\approx 5.8476088$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.17632698070846498 + \frac{1}{0.17632698070846498}$$

Expand \frac{1}{0.17632698070846498} by multiplying both numerator and the denominator by 100000000000000000.

$$0.17632698070846498+\frac{100000000000000000}{17632698070846498}$$

Reduce the fraction \frac{100000000000000000}{17632698070846498} to lowest terms by extracting and canceling out 2.

$$0.17632698070846498+\frac{50000000000000000}{8816349035423249}$$

Convert decimal number 0.17632698070846498 to fraction \frac{8816349035423249}{10000000000}. Reduce the fraction \frac{8816349035423249}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{8816349035423249}{50000000000000000}+\frac{50000000000000000}{8816349035423249}$$

Least common multiple of 50000000000000000 and 8816349035423249 is 440817451771162450000000000000000. Convert \frac{8816349035423249}{50000000000000000} and \frac{50000000000000000}{8816349035423249} to fractions with denominator 440817451771162450000000000000000.

$$\frac{77728010314408453050608569716001}{440817451771162450000000000000000}+\frac{2500000000000000000000000000000000}{440817451771162450000000000000000}$$

Since \frac{77728010314408453050608569716001}{440817451771162450000000000000000} and \frac{2500000000000000000000000000000000}{440817451771162450000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{77728010314408453050608569716001+2500000000000000000000000000000000}{440817451771162450000000000000000}$$

Add 77728010314408453050608569716001 and 2500000000000000000000000000000000 to get 2577728010314408453050608569716001.

$$\frac{2577728010314408453050608569716001}{440817451771162450000000000000000}$$