Solve cos285-sin255/sin525-sin705

$$\frac { \cos 285 - \sin 255 } { \sin 525 - \sin 705 }$$

Evaluate

$$\frac{122474487139158943}{51763809020504176}\approx 2.366025404$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.25881904510252113 - -0.9659258262890683}{0.2588190451025208 - -0.25881904510252096}$$

The opposite of -0.9659258262890683 is 0.9659258262890683.

$$\frac{0.25881904510252113+0.9659258262890683}{0.2588190451025208-\left(-0.25881904510252096\right)}$$

Add 0.25881904510252113 and 0.9659258262890683 to get 1.22474487139158943.

$$\frac{1.22474487139158943}{0.2588190451025208-\left(-0.25881904510252096\right)}$$

The opposite of -0.25881904510252096 is 0.25881904510252096.

$$\frac{1.22474487139158943}{0.2588190451025208+0.25881904510252096}$$

Add 0.2588190451025208 and 0.25881904510252096 to get 0.51763809020504176.

$$\frac{1.22474487139158943}{0.51763809020504176}$$

Expand \frac{1.22474487139158943}{0.51763809020504176} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{122474487139158943}{51763809020504176}$$

Factor

$$\frac{53 \cdot 1259 \cdot 1835456219209}{2027 \cdot 78467 \cdot 20340679 \cdot 2 ^ {4}} = 2\frac{18946869098150590}{51763809020504180} = 2.3660254037844384$$