Solve 1/tan(20^circ)-1/cos(10^circ)

$$\frac{ 1 }{ \tan ( 20 ^ { \circ } ) } - \frac{ 1 }{ \cos ( 10 ^ { \circ } ) }$$

Evaluate

$$\frac{1940117246081267687500000000000}{1120127214284455246620824431771}\approx 1.732050808$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1}{0.36397023426620234} - \frac{1}{0.984807753012208}$$

Expand \frac{1}{0.36397023426620234} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{100000000000000000}{36397023426620234}-\frac{1}{0.984807753012208}$$

Reduce the fraction \frac{100000000000000000}{36397023426620234} to lowest terms by extracting and canceling out 2.

$$\frac{50000000000000000}{18198511713310117}-\frac{1}{0.984807753012208}$$

Expand \frac{1}{0.984807753012208} by multiplying both numerator and the denominator by 1000000000000000.

$$\frac{50000000000000000}{18198511713310117}-\frac{1000000000000000}{984807753012208}$$

Reduce the fraction \frac{1000000000000000}{984807753012208} to lowest terms by extracting and canceling out 16.

$$\frac{50000000000000000}{18198511713310117}-\frac{62500000000000}{61550484563263}$$

Least common multiple of 18198511713310117 and 61550484563263 is 1120127214284455246620824431771. Convert \frac{50000000000000000}{18198511713310117} and \frac{62500000000000}{61550484563263} to fractions with denominator 1120127214284455246620824431771.

$$\frac{3077524228163150000000000000000}{1120127214284455246620824431771}-\frac{1137406982081882312500000000000}{1120127214284455246620824431771}$$

Since \frac{3077524228163150000000000000000}{1120127214284455246620824431771} and \frac{1137406982081882312500000000000}{1120127214284455246620824431771} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3077524228163150000000000000000-1137406982081882312500000000000}{1120127214284455246620824431771}$$

Subtract 1137406982081882312500000000000 from 3077524228163150000000000000000 to get 1940117246081267687500000000000.

$$\frac{1940117246081267687500000000000}{1120127214284455246620824431771}$$

Factor

$$\frac{11 \cdot 23 \cdot 122695161807511 \cdot 2 ^ {11} \cdot 5 ^ {15}}{7 \cdot 43 \cdot 443 \cdot 2399 \cdot 57915859 \cdot 60460171805017} = 1\frac{8.199900317968124 \times 10^{29}}{1.1201272142844552 \times 10^{30}} = 1.7320508075688774$$