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

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

Evaluer

$$-\frac{134004286912723150000000000000000}{1523745382982583587875356461647}\approx -87,944015063$$

Løsningsvejledning

Evaluate trigonometric functions in the problem

$$\frac{0,2680085738254463}{{(0,17364817766693033 - 0,3420201433256687 + 0,16327303458713335)} {(0,9396926207859084 - 0,3420201433256687)}}$$

Subtraher 0,3420201433256687 fra 0,17364817766693033 for at få -0,16837196565873837.

$$\frac{0,2680085738254463}{\left(-0,16837196565873837+0,16327303458713335\right)\left(0,9396926207859084-0,3420201433256687\right)}$$

Tilføj -0,16837196565873837 og 0,16327303458713335 for at få -0,00509893107160502.

$$\frac{0,2680085738254463}{-0,00509893107160502\left(0,9396926207859084-0,3420201433256687\right)}$$

Subtraher 0,3420201433256687 fra 0,9396926207859084 for at få 0,5976724774602397.

$$\frac{0,2680085738254463}{-0,00509893107160502\times 0,5976724774602397}$$

Multiplicer -0,00509893107160502 og 0,5976724774602397 for at få -0,003047490765965167175750712923294.

$$\frac{0,2680085738254463}{-0,003047490765965167175750712923294}$$

Udvid \frac{0,2680085738254463}{-0,003047490765965167175750712923294} ved at gange både tælleren og nævneren med 1000000000000000000000000000000000.

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

Reducer fraktionen \frac{268008573825446300000000000000000}{-3047490765965167175750712923294} til de laveste led ved at udtrække og annullere 2.

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

Faktoriser

$$-\frac{134004286912723150000000000000000}{1523745382982583587875356461647} = -87\frac{1,438438593238375 \times 10^{30}}{1,5237453829825836 \times 10^{30}} = -87,944015062689$$