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

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

Calcula

$$2,00000000000000025142552606969684$$

Passos de solució

Evaluate trigonometric functions in the problem

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

Multipliqueu 0,5150380749100542 per 1,9416040264103562 per obtenir 0,99999999999999988987361438330604.

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

Multipliqueu 0,6008606190275606 per 1,664279482350518 per obtenir 1,0000000000000003615519116863908.

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

Sumeu 0,99999999999999988987361438330604 més 1,0000000000000003615519116863908 per obtenir 2,00000000000000025142552606969684.

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

Obteniu el valor de \sin(30) de la taula de valors trigonomètrics.

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

Calculeu \frac{1}{2} elevat a 2 per obtenir \frac{1}{4}.

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

Multipliqueu 8 per \frac{1}{4} per obtenir 2.

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

Obteniu el valor de \tan(45) de la taula de valors trigonomètrics.

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

Calculeu 1 elevat a 2 per obtenir 1.

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

Resteu 2 de 1 per obtenir 1.

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

Qualsevol quantitat dividida entre u és igual a si mateixa.

$$2,00000000000000025142552606969684$$