다음을 풀어보세요: sin^{2}20^{circ}+cos^250^circ+sin20^circcos50^circ=3/4

$$\sin ^ { 2 } 20 ^ { \circ } + \cos ^ { 2 } 50 ^ { \circ } + \sin 20 ^ { \circ } \cos 50 ^ { \circ } = \frac { 3 } { 4 }$$

확인

해답 단계

Evaluate trigonometric functions in the problem

$$0.3420201433256687 ^ {2} + 0.6427876096865394 ^ {2} + 0.3420201433256687 \cdot 0.6427876096865394 = \frac{3}{4}$$

0.3420201433256687의 2제곱을 계산하여 0.11697777844051095979530830215969을(를) 구합니다.

$$0.11697777844051095979530830215969+0.6427876096865394^{2}+0.3420201433256687\times 0.6427876096865394=\frac{3}{4}$$

0.6427876096865394의 2제곱을 계산하여 0.41317591116653492029192554775236을(를) 구합니다.

$$0.11697777844051095979530830215969+0.41317591116653492029192554775236+0.3420201433256687\times 0.6427876096865394=\frac{3}{4}$$

0.11697777844051095979530830215969과(와) 0.41317591116653492029192554775236을(를) 더하여 0.53015368960704588008723384991205을(를) 구합니다.

$$0.53015368960704588008723384991205+0.3420201433256687\times 0.6427876096865394=\frac{3}{4}$$

0.3420201433256687과(와) 0.6427876096865394을(를) 곱하여 0.21984631039295419598585689389678(을)를 구합니다.

$$0.53015368960704588008723384991205+0.21984631039295419598585689389678=\frac{3}{4}$$

0.53015368960704588008723384991205과(와) 0.21984631039295419598585689389678을(를) 더하여 0.75000000000000007607309074380883을(를) 구합니다.

$$0.75000000000000007607309074380883=\frac{3}{4}$$

10진수 0.75000000000000007607309074380883을(를) 분수 \frac{75000000000000007607309074380883}{10000000000}(으)로 변환합니다. 1을(를) 추출 및 상쇄하여 분수 \frac{75000000000000007607309074380883}{10000000000}을(를) 기약 분수로 약분합니다.

$$\frac{75000000000000007607309074380883}{100000000000000000000000000000000}=\frac{3}{4}$$

100000000000000000000000000000000과(와) 4의 최소 공배수는 100000000000000000000000000000000입니다. \frac{75000000000000007607309074380883}{100000000000000000000000000000000} 및 \frac{3}{4}을(를) 분모 100000000000000000000000000000000의 분수로 변환합니다.

$$\frac{75000000000000007607309074380883}{100000000000000000000000000000000}=\frac{75000000000000000000000000000000}{100000000000000000000000000000000}$$

\frac{75000000000000007607309074380883}{100000000000000000000000000000000}과(와) \frac{75000000000000000000000000000000}{100000000000000000000000000000000}을(를) 비교합니다.

$$\text{false}$$