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

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

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$${(2)} \frac{0.17364817766693041}{0.3420201433256687} + 0.5150380749100543 \cdot 1.9416040264103567 = 2$$

Expand \frac{0.17364817766693041}{0.3420201433256687} by multiplying both numerator and the denominator by 100000000000000000.

$$2\times \frac{17364817766693041}{34202014332566870}+0.5150380749100543\times 1.9416040264103567=2$$

Express 2\times \frac{17364817766693041}{34202014332566870} as a single fraction.

$$\frac{2\times 17364817766693041}{34202014332566870}+0.5150380749100543\times 1.9416040264103567=2$$

Multiply 2 and 17364817766693041 to get 34729635533386082.

$$\frac{34729635533386082}{34202014332566870}+0.5150380749100543\times 1.9416040264103567=2$$

Reduce the fraction \frac{34729635533386082}{34202014332566870} to lowest terms by extracting and canceling out 2.

$$\frac{17364817766693041}{17101007166283435}+0.5150380749100543\times 1.9416040264103567=2$$

Multiply 0.5150380749100543 and 1.9416040264103567 to get 1.00000000000000034155305447936881.

$$\frac{17364817766693041}{17101007166283435}+1.00000000000000034155305447936881=2$$

Convert decimal number 1.00000000000000034155305447936881 to fraction \frac{100000000000000034155305447936881}{10000000000}. Reduce the fraction \frac{100000000000000034155305447936881}{10000000000} to lowest terms by extracting and canceling out 1.

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

Least common multiple of 17101007166283435 and 100000000000000000000000000000000 is 342020143325668700000000000000000000000000000000. Convert \frac{17364817766693041}{17101007166283435} and \frac{100000000000000034155305447936881}{100000000000000000000000000000000} to fractions with denominator 342020143325668700000000000000000000000000000000.

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

Since \frac{347296355333860820000000000000000000000000000000}{342020143325668700000000000000000000000000000000} and \frac{342020143325668816818024646353650179265047173247}{342020143325668700000000000000000000000000000000} have the same denominator, add them by adding their numerators.

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

Add 347296355333860820000000000000000000000000000000 and 342020143325668816818024646353650179265047173247 to get 689316498659529636818024646353650179265047173247.

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

Convert 2 to fraction \frac{684040286651337400000000000000000000000000000000}{342020143325668700000000000000000000000000000000}.

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

Compare \frac{689316498659529636818024646353650179265047173247}{342020143325668700000000000000000000000000000000} and \frac{684040286651337400000000000000000000000000000000}{342020143325668700000000000000000000000000000000}.

$$\text{false}$$