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

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

Calcular

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

Pasos da solución

Evaluate trigonometric functions in the problem

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

Resta 0.3420201433256687 de 0.17364817766693033 para obter -0.16837196565873837.

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

Suma -0.16837196565873837 e 0.16327303458713335 para obter -0.00509893107160502.

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

Resta 0.3420201433256687 de 0.9396926207859084 para obter 0.5976724774602397.

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

Multiplica -0.00509893107160502 e 0.5976724774602397 para obter -0.003047490765965167175750712923294.

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

Expande \frac{0.2680085738254463}{-0.003047490765965167175750712923294} multiplicando o numerador e o denominador por 1000000000000000000000000000000000.

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

Reduce a fracción \frac{268008573825446300000000000000000}{-3047490765965167175750712923294} a termos máis baixos extraendo e cancelando 2.

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