Solve 2cos(150^circ-10^circ)-sin10^circ/cos10^circ

$$\frac { 2 \cos ( 150 ^ { \circ } - 10 ^ { \circ } ) - \sin 10 ^ { \circ } } { \cos 10 ^ { \circ } }$$

Evaluate

$$-\frac{170573706390488613}{98480775301220800}\approx -1.732050808$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{2 \cdot -0.7660444431189779 - 0.17364817766693033}{0.984807753012208}$$

Multiply 2 and -0.7660444431189779 to get -1.5320888862379558.

$$\frac{-1.5320888862379558-0.17364817766693033}{0.984807753012208}$$

Subtract 0.17364817766693033 from -1.5320888862379558 to get -1.70573706390488613.

$$\frac{-1.70573706390488613}{0.984807753012208}$$

Expand \frac{-1.70573706390488613}{0.984807753012208} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{-170573706390488613}{98480775301220800}$$

Fraction \frac{-170573706390488613}{98480775301220800} can be rewritten as -\frac{170573706390488613}{98480775301220800} by extracting the negative sign.

$$-\frac{170573706390488613}{98480775301220800}$$

Factor

$$-\frac{170573706390488613}{98480775301220800} = -1\frac{72092931089267800}{98480775301220800} = -1.732050807568877$$