Solve 2cos20-sin10/cos10

$$\frac { 2 \cos 20 - \sin 10 } { \cos 10 }$$

Evaluate

$$\frac{170573706390488647}{98480775301220800}\approx 1.732050808$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{2 \cdot 0.9396926207859084 - 0.17364817766693033}{0.984807753012208}$$

Multiply 2 and 0.9396926207859084 to get 1.8793852415718168.

$$\frac{1.8793852415718168-0.17364817766693033}{0.984807753012208}$$

Subtract 0.17364817766693033 from 1.8793852415718168 to get 1.70573706390488647.

$$\frac{1.70573706390488647}{0.984807753012208}$$

Expand \frac{1.70573706390488647}{0.984807753012208} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{170573706390488647}{98480775301220800}$$

Factor

$$\frac{23 \cdot 1747 \cdot 2039 \cdot 3581 \cdot 581393}{443 \cdot 2399 \cdot 57915859 \cdot 2 ^ {6} \cdot 5 ^ {2}} = 1\frac{72092931089267840}{98480775301220800} = 1.7320508075688774$$