Solve 21*cos50^circ-1-sin10^circ/cos10^circ

$$21 \cdot \cos 50 ^ { \circ } - \frac { 1 - \sin 10 ^ { \circ } } { \cos 10 ^ { \circ } }$$

Evaluate

$$\frac{3895973384505062631868578416531}{307752422816315000000000000000}\approx 12.659440172$$

Solution Steps

Evaluate trigonometric functions in the problem

$$21 \cdot 0.6427876096865394 - \frac{1 - 0.17364817766693033}{0.984807753012208}$$

Multiply 21 and 0.6427876096865394 to get 13.4985398034173274.

$$13.4985398034173274-\frac{1-0.17364817766693033}{0.984807753012208}$$

Subtract 0.17364817766693033 from 1 to get 0.82635182233306967.

$$13.4985398034173274-\frac{0.82635182233306967}{0.984807753012208}$$

Expand \frac{0.82635182233306967}{0.984807753012208} by multiplying both numerator and the denominator by 100000000000000000.

$$13.4985398034173274-\frac{82635182233306967}{98480775301220800}$$

Convert decimal number 13.4985398034173274 to fraction \frac{67492699017086637}{10000000000}. Reduce the fraction \frac{67492699017086637}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{67492699017086637}{5000000000000000}-\frac{82635182233306967}{98480775301220800}$$

Least common multiple of 5000000000000000 and 98480775301220800 is 307752422816315000000000000000. Convert \frac{67492699017086637}{5000000000000000} and \frac{82635182233306967}{98480775301220800} to fractions with denominator 307752422816315000000000000000.

$$\frac{4154208328984146903743578416531}{307752422816315000000000000000}-\frac{258234944479084271875000000000}{307752422816315000000000000000}$$

Since \frac{4154208328984146903743578416531}{307752422816315000000000000000} and \frac{258234944479084271875000000000}{307752422816315000000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4154208328984146903743578416531-258234944479084271875000000000}{307752422816315000000000000000}$$

Subtract 258234944479084271875000000000 from 4154208328984146903743578416531 to get 3895973384505062631868578416531.

$$\frac{3895973384505062631868578416531}{307752422816315000000000000000}$$

Factor

$$\frac{37 \cdot 719 \cdot 3257 \cdot 44964276348233925751361}{443 \cdot 2399 \cdot 57915859 \cdot 2 ^ {15} \cdot 5 ^ {16}} = 12\frac{2.0294431070928294 \times 10^{29}}{3.07752422816315 \times 10^{29}} = 12.659440172240048$$