Solve frac{cos8^{circ}+sin8^circ}{cos8^circ-sin8^circ}=tan53^circ

$$\frac { \cos 8 ^ { \circ } + \sin 8 ^ { \circ } } { \cos 8 ^ { \circ } - \sin 8 ^ { \circ } } = \tan 53 ^ { \circ }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.9902680687415704 + 0.13917310096006544}{0.9902680687415704 - 0.13917310096006544} = 1.3270448216204098$$

Add 0.9902680687415704 and 0.13917310096006544 to get 1.12944116970163584.

$$\frac{1.12944116970163584}{0.9902680687415704-0.13917310096006544}=1.3270448216204098$$

Subtract 0.13917310096006544 from 0.9902680687415704 to get 0.85109496778150496.

$$\frac{1.12944116970163584}{0.85109496778150496}=1.3270448216204098$$

Expand \frac{1.12944116970163584}{0.85109496778150496} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{112944116970163584}{85109496778150496}=1.3270448216204098$$

Reduce the fraction \frac{112944116970163584}{85109496778150496} to lowest terms by extracting and canceling out 32.

$$\frac{3529503655317612}{2659671774317203}=1.3270448216204098$$

Convert decimal number 1.3270448216204098 to fraction \frac{6635224108102049}{10000000000}. Reduce the fraction \frac{6635224108102049}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{3529503655317612}{2659671774317203}=\frac{6635224108102049}{5000000000000000}$$

Least common multiple of 2659671774317203 and 5000000000000000 is 13298358871586015000000000000000. Convert \frac{3529503655317612}{2659671774317203} and \frac{6635224108102049}{5000000000000000} to fractions with denominator 13298358871586015000000000000000.

$$\frac{17647518276588060000000000000000}{13298358871586015000000000000000}=\frac{17647518276588057429627220248947}{13298358871586015000000000000000}$$

Compare \frac{17647518276588060000000000000000}{13298358871586015000000000000000} and \frac{17647518276588057429627220248947}{13298358871586015000000000000000}.

$$\text{false}$$