Resolver 30^{circ}+frac{sin31^{circ}sec59^{circ}+cot59^{circ}cot31^{circ}}{8sin^230^circ-tan^245^circ}

$$30 ^ { \circ } + \frac { \sin 31 ^ { \circ } \sec 59 ^ { \circ } + \cot 59 ^ { \circ } \cot 31 ^ { \circ } } { 8 \sin ^ { 2 } 30 ^ { \circ } - \tan ^ { 2 } 45 ^ { \circ } }$$

Avaliar

$$32,00000000000000025142552606969684$$

Passos Para a Resolução

Evaluate trigonometric functions in the problem

$$30 + \frac{0,5150380749100542 \cdot 1,9416040264103562 + 0,6008606190275606 \cdot 1,664279482350518}{8 \sin^{2}(30) - \tan^{2}(45)}$$

Multiplique 0,5150380749100542 e 1,9416040264103562 para obter 0,99999999999999988987361438330604.

$$30+\frac{0,99999999999999988987361438330604+0,6008606190275606\times 1,664279482350518}{8\left(\sin(30)\right)^{2}-\left(\tan(45)\right)^{2}}$$

Multiplique 0,6008606190275606 e 1,664279482350518 para obter 1,0000000000000003615519116863908.

$$30+\frac{0,99999999999999988987361438330604+1,0000000000000003615519116863908}{8\left(\sin(30)\right)^{2}-\left(\tan(45)\right)^{2}}$$

Some 0,99999999999999988987361438330604 e 1,0000000000000003615519116863908 para obter 2,00000000000000025142552606969684.

$$30+\frac{2,00000000000000025142552606969684}{8\left(\sin(30)\right)^{2}-\left(\tan(45)\right)^{2}}$$

Obtenha o valor de \sin(30) a partir da tabela de valores trigonométricos.

$$30+\frac{2,00000000000000025142552606969684}{8\times \left(\frac{1}{2}\right)^{2}-\left(\tan(45)\right)^{2}}$$

Calcule \frac{1}{2} elevado a 2 e obtenha \frac{1}{4}.

$$30+\frac{2,00000000000000025142552606969684}{8\times \frac{1}{4}-\left(\tan(45)\right)^{2}}$$

Multiplique 8 e \frac{1}{4} para obter 2.

$$30+\frac{2,00000000000000025142552606969684}{2-\left(\tan(45)\right)^{2}}$$

Obtenha o valor de \tan(45) a partir da tabela de valores trigonométricos.

$$30+\frac{2,00000000000000025142552606969684}{2-1^{2}}$$

Calcule 1 elevado a 2 e obtenha 1.

$$30+\frac{2,00000000000000025142552606969684}{2-1}$$

Subtraia 1 de 2 para obter 1.

$$30+\frac{2,00000000000000025142552606969684}{1}$$

Qualquer número dividido por um resulta no próprio número.

$$30+2,00000000000000025142552606969684$$

Some 30 e 2,00000000000000025142552606969684 para obter 32,00000000000000025142552606969684.

$$32,00000000000000025142552606969684$$