Solve 2sin70^circ+3cos20^circ-3/cos20^circ

$$2 \sin 70 ^ { \circ } + 3 \cos 20 ^ { \circ } - \frac { 3 } { \cos 20 ^ { \circ } }$$

Evaluate

$$\frac{5896296282489354374624232953213}{3915385919941285000000000000000}\approx 1.505929787$$

Solution Steps

Evaluate trigonometric functions in the problem

$$2 \cdot 0.9396926207859083 + 3 \cdot 0.9396926207859084 - \frac{3}{0.9396926207859084}$$

Multiply 2 and 0.9396926207859083 to get 1.8793852415718166.

$$1.8793852415718166+3\times 0.9396926207859084-\frac{3}{0.9396926207859084}$$

Multiply 3 and 0.9396926207859084 to get 2.8190778623577252.

$$1.8793852415718166+2.8190778623577252-\frac{3}{0.9396926207859084}$$

Add 1.8793852415718166 and 2.8190778623577252 to get 4.6984631039295418.

$$4.6984631039295418-\frac{3}{0.9396926207859084}$$

Expand \frac{3}{0.9396926207859084} by multiplying both numerator and the denominator by 10000000000000000.

$$4.6984631039295418-\frac{30000000000000000}{9396926207859084}$$

Reduce the fraction \frac{30000000000000000}{9396926207859084} to lowest terms by extracting and canceling out 12.

$$4.6984631039295418-\frac{2500000000000000}{783077183988257}$$

Convert decimal number 4.6984631039295418 to fraction \frac{23492315519647709}{10000000000}. Reduce the fraction \frac{23492315519647709}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{23492315519647709}{5000000000000000}-\frac{2500000000000000}{783077183988257}$$

Least common multiple of 5000000000000000 and 783077183988257 is 3915385919941285000000000000000. Convert \frac{23492315519647709}{5000000000000000} and \frac{2500000000000000}{783077183988257} to fractions with denominator 3915385919941285000000000000000.

$$\frac{18396296282489354374624232953213}{3915385919941285000000000000000}-\frac{12500000000000000000000000000000}{3915385919941285000000000000000}$$

Since \frac{18396296282489354374624232953213}{3915385919941285000000000000000} and \frac{12500000000000000000000000000000}{3915385919941285000000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18396296282489354374624232953213-12500000000000000000000000000000}{3915385919941285000000000000000}$$

Subtract 12500000000000000000000000000000 from 18396296282489354374624232953213 to get 5896296282489354374624232953213.

$$\frac{5896296282489354374624232953213}{3915385919941285000000000000000}$$