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

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

Laske

$$2,00000000000000025142552606969684$$

Ratkaisun vaiheet

Evaluate trigonometric functions in the problem

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

Kerro 0,5150380749100542 ja 1,9416040264103562, niin saadaan 0,99999999999999988987361438330604.

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

Kerro 0,6008606190275606 ja 1,664279482350518, niin saadaan 1,0000000000000003615519116863908.

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

Selvitä 2,00000000000000025142552606969684 laskemalla yhteen 0,99999999999999988987361438330604 ja 1,0000000000000003615519116863908.

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

Hae kaavan \sin(30) arvo trigonometristen arvojen taulukosta.

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

Laske \frac{1}{2} potenssiin 2, jolloin ratkaisuksi tulee \frac{1}{4}.

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

Kerro 8 ja \frac{1}{4}, niin saadaan 2.

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

Hae kaavan \tan(45) arvo trigonometristen arvojen taulukosta.

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

Laske 1 potenssiin 2, jolloin ratkaisuksi tulee 1.

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

Vähennä 1 luvusta 2 saadaksesi tuloksen 1.

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

Luvun jakaminen yhdellä antaa tulokseksi alkuperäisen luvun.

$$2,00000000000000025142552606969684$$