Solve tan(75)+1/tan(75)

$$\tan ( 75 ) + \frac{ 1 }{ \tan ( 75 ) }$$

Evaluate

$$\frac{23325317547305486658831356443409}{5831329386826371250000000000000}\approx 4$$

Solution Steps

Evaluate trigonometric functions in the problem

$$3.7320508075688776 + \frac{1}{3.7320508075688776}$$

Expand \frac{1}{3.7320508075688776} by multiplying both numerator and the denominator by 10000000000000000.

$$3.7320508075688776+\frac{10000000000000000}{37320508075688776}$$

Reduce the fraction \frac{10000000000000000}{37320508075688776} to lowest terms by extracting and canceling out 8.

$$3.7320508075688776+\frac{1250000000000000}{4665063509461097}$$

Convert decimal number 3.7320508075688776 to fraction \frac{4665063509461097}{10000000000}. Reduce the fraction \frac{4665063509461097}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{4665063509461097}{1250000000000000}+\frac{1250000000000000}{4665063509461097}$$

Least common multiple of 1250000000000000 and 4665063509461097 is 5831329386826371250000000000000. Convert \frac{4665063509461097}{1250000000000000} and \frac{1250000000000000}{4665063509461097} to fractions with denominator 5831329386826371250000000000000.

$$\frac{21762817547305486658831356443409}{5831329386826371250000000000000}+\frac{1562500000000000000000000000000}{5831329386826371250000000000000}$$

Since \frac{21762817547305486658831356443409}{5831329386826371250000000000000} and \frac{1562500000000000000000000000000}{5831329386826371250000000000000} have the same denominator, add them by adding their numerators.

$$\frac{21762817547305486658831356443409+1562500000000000000000000000000}{5831329386826371250000000000000}$$

Add 21762817547305486658831356443409 and 1562500000000000000000000000000 to get 23325317547305486658831356443409.

$$\frac{23325317547305486658831356443409}{5831329386826371250000000000000}$$

Factor

$$\frac{1217 \cdot 6833 \cdot 127837 \cdot 3020546449 \cdot 7264127813}{23 \cdot 149011 \cdot 1361166949 \cdot 2 ^ {13} \cdot 5 ^ {16}} = 4$$