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

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

Meta

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

Lausnarskref

Evaluate trigonometric functions in the problem

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

Dragðu 0.3420201433256687 frá 0.17364817766693033 til að fá út -0.16837196565873837.

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

Leggðu saman -0.16837196565873837 og 0.16327303458713335 til að fá -0.00509893107160502.

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

Dragðu 0.3420201433256687 frá 0.9396926207859084 til að fá út 0.5976724774602397.

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

Margfaldaðu -0.00509893107160502 og 0.5976724774602397 til að fá út -0.003047490765965167175750712923294.

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

Leystu upp \frac{0.2680085738254463}{-0.003047490765965167175750712923294} með því að margfalda bæði teljara og nefnara með 1000000000000000000000000000000000.

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

Minnka brotið \frac{268008573825446300000000000000000}{-3047490765965167175750712923294} eins mikið og hægt er með því að draga og stytta út 2.

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