Solve frac{sin20^{circ}(tan10^{circ}*sin410^{circ}+sin860^{circ})}{(sin10^{circ}-sin20^{circ}+sin10^circ*cos20^circ)(cos20^circ-sin20^circ)}

$$\frac { \sin 20 ^ { \circ } ( \tan 10 ^ { \circ } \cdot \sin 410 ^ { \circ } + \sin 860 ^ { \circ } ) } { ( \sin 10 ^ { \circ } - \sin 20 ^ { \circ } + \sin 10 ^ { \circ } \cdot \cos 20 ^ { \circ } ) ( \cos 20 ^ { \circ } - \sin 20 ^ { \circ } ) }$$

Evaluate

$$-\frac{134004286912723150000000000000000}{1523745382982583587875356461647}\approx -87.944015063$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.2680085738254463}{{(0.17364817766693033 - 0.3420201433256687 + 0.16327303458713335)} {(0.9396926207859084 - 0.3420201433256687)}}$$

Subtract 0.3420201433256687 from 0.17364817766693033 to get -0.16837196565873837.

$$\frac{0.2680085738254463}{\left(-0.16837196565873837+0.16327303458713335\right)\left(0.9396926207859084-0.3420201433256687\right)}$$

Add -0.16837196565873837 and 0.16327303458713335 to get -0.00509893107160502.

$$\frac{0.2680085738254463}{-0.00509893107160502\left(0.9396926207859084-0.3420201433256687\right)}$$

Subtract 0.3420201433256687 from 0.9396926207859084 to get 0.5976724774602397.

$$\frac{0.2680085738254463}{-0.00509893107160502\times 0.5976724774602397}$$

Multiply -0.00509893107160502 and 0.5976724774602397 to get -0.003047490765965167175750712923294.

$$\frac{0.2680085738254463}{-0.003047490765965167175750712923294}$$

Expand \frac{0.2680085738254463}{-0.003047490765965167175750712923294} by multiplying both numerator and the denominator by 1000000000000000000000000000000000.

$$\frac{268008573825446300000000000000000}{-3047490765965167175750712923294}$$

Reduce the fraction \frac{268008573825446300000000000000000}{-3047490765965167175750712923294} to lowest terms by extracting and canceling out 2.

$$-\frac{134004286912723150000000000000000}{1523745382982583587875356461647}$$

Factor

$$-\frac{134004286912723150000000000000000}{1523745382982583587875356461647} = -87\frac{1.438438593238375 \times 10^{30}}{1.5237453829825836 \times 10^{30}} = -87.944015062689$$