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

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

Verificar

Pasos da solución

Evaluate trigonometric functions in the problem

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

Calcula 0.3420201433256687 á potencia de 2 e obtén 0.11697777844051095979530830215969.

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

Calcula 0.6427876096865394 á potencia de 2 e obtén 0.41317591116653492029192554775236.

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

Suma 0.11697777844051095979530830215969 e 0.41317591116653492029192554775236 para obter 0.53015368960704588008723384991205.

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

Multiplica 0.3420201433256687 e 0.6427876096865394 para obter 0.21984631039295419598585689389678.

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

Suma 0.53015368960704588008723384991205 e 0.21984631039295419598585689389678 para obter 0.75000000000000007607309074380883.

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

Converte o número decimal 0.75000000000000007607309074380883 á fracción \frac{75000000000000007607309074380883}{10000000000}. Reduce a fracción \frac{75000000000000007607309074380883}{10000000000} a termos máis baixos extraendo e cancelando 1.

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

O mínimo común múltiplo de 100000000000000000000000000000000 e 4 é 100000000000000000000000000000000. Converte \frac{75000000000000007607309074380883}{100000000000000000000000000000000} e \frac{3}{4} a fraccións co denominador 100000000000000000000000000000000.

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

Comparar \frac{75000000000000007607309074380883}{100000000000000000000000000000000} e \frac{75000000000000000000000000000000}{100000000000000000000000000000000}.

$$\text{false}$$