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

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

Calcular

$$32.00000000000000025142552606969684$$

Pasos da solución

Evaluate trigonometric functions in the problem

$$30 + \frac{0.5150380749100542 \cdot 1.9416040264103562 + 0.6008606190275606 \cdot 1.664279482350518}{8 \sin^{2}(30) - \tan^{2}(45)}$$

Multiplica 0.5150380749100542 e 1.9416040264103562 para obter 0.99999999999999988987361438330604.

$$30+\frac{0.99999999999999988987361438330604+0.6008606190275606\times 1.664279482350518}{8\left(\sin(30)\right)^{2}-\left(\tan(45)\right)^{2}}$$

Multiplica 0.6008606190275606 e 1.664279482350518 para obter 1.0000000000000003615519116863908.

$$30+\frac{0.99999999999999988987361438330604+1.0000000000000003615519116863908}{8\left(\sin(30)\right)^{2}-\left(\tan(45)\right)^{2}}$$

Suma 0.99999999999999988987361438330604 e 1.0000000000000003615519116863908 para obter 2.00000000000000025142552606969684.

$$30+\frac{2.00000000000000025142552606969684}{8\left(\sin(30)\right)^{2}-\left(\tan(45)\right)^{2}}$$

Obtén o valor de \sin(30) a partir da táboa de valores trigonométricos.

$$30+\frac{2.00000000000000025142552606969684}{8\times \left(\frac{1}{2}\right)^{2}-\left(\tan(45)\right)^{2}}$$

Calcula \frac{1}{2} á potencia de 2 e obtén \frac{1}{4}.

$$30+\frac{2.00000000000000025142552606969684}{8\times \frac{1}{4}-\left(\tan(45)\right)^{2}}$$

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

$$30+\frac{2.00000000000000025142552606969684}{2-\left(\tan(45)\right)^{2}}$$

Obtén o valor de \tan(45) a partir da táboa de valores trigonométricos.

$$30+\frac{2.00000000000000025142552606969684}{2-1^{2}}$$

Calcula 1 á potencia de 2 e obtén 1.

$$30+\frac{2.00000000000000025142552606969684}{2-1}$$

Resta 1 de 2 para obter 1.

$$30+\frac{2.00000000000000025142552606969684}{1}$$

Calquera cifra entre un é igual á cifra.

$$30+2.00000000000000025142552606969684$$

Suma 30 e 2.00000000000000025142552606969684 para obter 32.00000000000000025142552606969684.

$$32.00000000000000025142552606969684$$