Solve tan54^{circ}=cos9^circ+sin9^circ/cos9^circ-sin9^circ

$$\tan 54 ^ { \circ } = \frac { \cos 9 ^ { \circ } + \sin 9 ^ { \circ } } { \cos 9 ^ { \circ } - \sin 9 ^ { \circ } }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$1.3763819204711734 = \frac{0.9876883405951378 + 0.15643446504023087}{0.9876883405951378 - 0.15643446504023087}$$

Add 0.9876883405951378 and 0.15643446504023087 to get 1.14412280563536867.

$$1.3763819204711734=\frac{1.14412280563536867}{0.9876883405951378-0.15643446504023087}$$

Subtract 0.15643446504023087 from 0.9876883405951378 to get 0.83125387555490693.

$$1.3763819204711734=\frac{1.14412280563536867}{0.83125387555490693}$$

Expand \frac{1.14412280563536867}{0.83125387555490693} by multiplying both numerator and the denominator by 100000000000000000.

$$1.3763819204711734=\frac{114412280563536867}{83125387555490693}$$

Convert decimal number 1.3763819204711734 to fraction \frac{6881909602355867}{10000000000}. Reduce the fraction \frac{6881909602355867}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{6881909602355867}{5000000000000000}=\frac{114412280563536867}{83125387555490693}$$

Least common multiple of 5000000000000000 and 83125387555490693 is 415626937777453465000000000000000. Convert \frac{6881909602355867}{5000000000000000} and \frac{114412280563536867}{83125387555490693} to fractions with denominator 415626937777453465000000000000000.

$$\frac{572061402817684290271543992445831}{415626937777453465000000000000000}=\frac{572061402817684335000000000000000}{415626937777453465000000000000000}$$

Compare \frac{572061402817684290271543992445831}{415626937777453465000000000000000} and \frac{572061402817684335000000000000000}{415626937777453465000000000000000}.

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