Solve frac{cos37^{circ}+sin37^circ}{cos37^circ-sin37^circ}=cot8^circ

$$\frac { \cos 37 ^ { \circ } + \sin 37 ^ { \circ } } { \cos 37 ^ { \circ } - \sin 37 ^ { \circ } } = \cot 8 ^ { \circ }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.7986355100472928 + 0.6018150231520483}{0.7986355100472928 - 0.6018150231520483} = 7.115369722384209$$

Add 0.7986355100472928 and 0.6018150231520483 to get 1.4004505331993411.

$$\frac{1.4004505331993411}{0.7986355100472928-0.6018150231520483}=7.115369722384209$$

Subtract 0.6018150231520483 from 0.7986355100472928 to get 0.1968204868952445.

$$\frac{1.4004505331993411}{0.1968204868952445}=7.115369722384209$$

Expand \frac{1.4004505331993411}{0.1968204868952445} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{14004505331993411}{1968204868952445}=7.115369722384209$$

Convert decimal number 7.115369722384209 to fraction \frac{7115369722384209}{10000000000}. Reduce the fraction \frac{7115369722384209}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{14004505331993411}{1968204868952445}=\frac{7115369722384209}{1000000000000000}$$

Least common multiple of 1968204868952445 and 1000000000000000 is 393640973790489000000000000000. Convert \frac{14004505331993411}{1968204868952445} and \frac{7115369722384209}{1000000000000000} to fractions with denominator 393640973790489000000000000000.

$$\frac{2800901066398682200000000000000}{393640973790489000000000000000}=\frac{2800901066398681407073127988201}{393640973790489000000000000000}$$

Compare \frac{2800901066398682200000000000000}{393640973790489000000000000000} and \frac{2800901066398681407073127988201}{393640973790489000000000000000}.

$$\text{false}$$