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

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

계산

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

해답 단계

Evaluate trigonometric functions in the problem

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

0.17364817766693033에서 0.3420201433256687을(를) 빼고 -0.16837196565873837을(를) 구합니다.

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

-0.16837196565873837과(와) 0.16327303458713335을(를) 더하여 -0.00509893107160502을(를) 구합니다.

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

0.9396926207859084에서 0.3420201433256687을(를) 빼고 0.5976724774602397을(를) 구합니다.

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

-0.00509893107160502과(와) 0.5976724774602397을(를) 곱하여 -0.003047490765965167175750712923294(을)를 구합니다.

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

분자와 분모 모두에 1000000000000000000000000000000000을(를) 곱하여 \frac{0.2680085738254463}{-0.003047490765965167175750712923294}을(를) 확장합니다.

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

2을(를) 추출 및 상쇄하여 분수 \frac{268008573825446300000000000000000}{-3047490765965167175750712923294}을(를) 기약 분수로 약분합니다.

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