Solve sin34/cos56^circ+cos43/sin47

$$\frac { \sin 34 } { \cos 56 ^ { \circ } } + \frac { \cos 43 } { \sin 47 }$$

Evaluate

$$\frac{81793559974500446315934217205053}{40896779987250216705234083152940}\approx 2$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.5591929034707469}{0.5591929034707468} + \frac{0.7313537016191706}{0.7313537016191705}$$

Expand \frac{0.5591929034707469}{0.5591929034707468} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{5591929034707469}{5591929034707468}+\frac{0.7313537016191706}{0.7313537016191705}$$

Expand \frac{0.7313537016191706}{0.7313537016191705} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{5591929034707469}{5591929034707468}+\frac{7313537016191706}{7313537016191705}$$

Least common multiple of 5591929034707468 and 7313537016191705 is 40896779987250216705234083152940. Convert \frac{5591929034707469}{5591929034707468} and \frac{7313537016191706}{7313537016191705} to fractions with denominator 40896779987250216705234083152940.

$$\frac{40896779987250224018771099344645}{40896779987250216705234083152940}+\frac{40896779987250222297163117860408}{40896779987250216705234083152940}$$

Since \frac{40896779987250224018771099344645}{40896779987250216705234083152940} and \frac{40896779987250222297163117860408}{40896779987250216705234083152940} have the same denominator, add them by adding their numerators.

$$\frac{40896779987250224018771099344645+40896779987250222297163117860408}{40896779987250216705234083152940}$$

Add 40896779987250224018771099344645 and 40896779987250222297163117860408 to get 81793559974500446315934217205053.

$$\frac{81793559974500446315934217205053}{40896779987250216705234083152940}$$

Factor

$$\frac{34679 \cdot 45959 \cdot 683534857 \cdot 75079489010389}{5 \cdot 13 \cdot 19 \cdot 229 \cdot 8647 \cdot 684849349 \cdot 6104726020423 \cdot 2 ^ {2}} = 2\frac{18014398509481984}{4.089677998725022 \times 10^{31}} = 2.0000000000000004$$