Ratkaise (2)cos80^circ/sin20^circ+cos59^circcsc31^circ=2

$$( 2 ) \frac { \cos 80 ^ { \circ } } { \sin 20 ^ { \circ } } + \cos 59 ^ { \circ } \csc 31 ^ { \circ } = 2$$

Tarkista

Ratkaisun vaiheet

Evaluate trigonometric functions in the problem

$${(2)} \frac{0,17364817766693041}{0,3420201433256687} + 0,5150380749100543 \cdot 1,9416040264103567 = 2$$

Lavenna \frac{0,17364817766693041}{0,3420201433256687} kertomalla sekä osoittaja että nimittäjä luvulla 100000000000000000.

$$2\times \frac{17364817766693041}{34202014332566870}+0,5150380749100543\times 1,9416040264103567=2$$

Ilmaise 2\times \frac{17364817766693041}{34202014332566870} säännöllisenä murtolukuna.

$$\frac{2\times 17364817766693041}{34202014332566870}+0,5150380749100543\times 1,9416040264103567=2$$

Kerro 2 ja 17364817766693041, niin saadaan 34729635533386082.

$$\frac{34729635533386082}{34202014332566870}+0,5150380749100543\times 1,9416040264103567=2$$

Supista murtoluku \frac{34729635533386082}{34202014332566870} luvulla 2.

$$\frac{17364817766693041}{17101007166283435}+0,5150380749100543\times 1,9416040264103567=2$$

Kerro 0,5150380749100543 ja 1,9416040264103567, niin saadaan 1,00000000000000034155305447936881.

$$\frac{17364817766693041}{17101007166283435}+1,00000000000000034155305447936881=2$$

Muunna desimaaliluku 1,00000000000000034155305447936881 murtoluvuksi \frac{100000000000000034155305447936881}{10000000000}. Supista murtoluku \frac{100000000000000034155305447936881}{10000000000} luvulla 1.

$$\frac{17364817766693041}{17101007166283435}+\frac{100000000000000034155305447936881}{100000000000000000000000000000000}=2$$

Lukujen 17101007166283435 ja 100000000000000000000000000000000 pienin yhteinen jaettava on 342020143325668700000000000000000000000000000000. Muunna \frac{17364817766693041}{17101007166283435} ja \frac{100000000000000034155305447936881}{100000000000000000000000000000000} murtoluvuiksi, joiden nimittäjä on 342020143325668700000000000000000000000000000000.

$$\frac{347296355333860820000000000000000000000000000000}{342020143325668700000000000000000000000000000000}+\frac{342020143325668816818024646353650179265047173247}{342020143325668700000000000000000000000000000000}=2$$

Koska arvoilla \frac{347296355333860820000000000000000000000000000000}{342020143325668700000000000000000000000000000000} ja \frac{342020143325668816818024646353650179265047173247}{342020143325668700000000000000000000000000000000} on sama nimittäjä, laske ne yhteen laskemalla niiden osoittajat yhteen.

$$\frac{347296355333860820000000000000000000000000000000+342020143325668816818024646353650179265047173247}{342020143325668700000000000000000000000000000000}=2$$

Selvitä 689316498659529636818024646353650179265047173247 laskemalla yhteen 347296355333860820000000000000000000000000000000 ja 342020143325668816818024646353650179265047173247.

$$\frac{689316498659529636818024646353650179265047173247}{342020143325668700000000000000000000000000000000}=2$$

Muunna 2 murtoluvuksi \frac{684040286651337400000000000000000000000000000000}{342020143325668700000000000000000000000000000000}.

$$\frac{689316498659529636818024646353650179265047173247}{342020143325668700000000000000000000000000000000}=\frac{684040286651337400000000000000000000000000000000}{342020143325668700000000000000000000000000000000}$$

Vertaa kohteita \frac{689316498659529636818024646353650179265047173247}{342020143325668700000000000000000000000000000000} ja \frac{684040286651337400000000000000000000000000000000}{342020143325668700000000000000000000000000000000}.

$$\text{false}$$