Solve tan(58^circ)=1+2tan(29^circ)/1-tan(29^circ)

$$\tan ( 58 ^ { \circ } ) = \frac { 1 + 2 \tan ( 29 ^ { \circ } ) } { 1 - \tan ( 29 ^ { \circ } ) }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$1.6003345290410507 = \frac{1 + 2 \cdot 0.554309051452769}{1 - 0.554309051452769}$$

Multiply 2 and 0.554309051452769 to get 1.108618102905538.

$$1.6003345290410507=\frac{1+1.108618102905538}{1-0.554309051452769}$$

Add 1 and 1.108618102905538 to get 2.108618102905538.

$$1.6003345290410507=\frac{2.108618102905538}{1-0.554309051452769}$$

Subtract 0.554309051452769 from 1 to get 0.445690948547231.

$$1.6003345290410507=\frac{2.108618102905538}{0.445690948547231}$$

Expand \frac{2.108618102905538}{0.445690948547231} by multiplying both numerator and the denominator by 1000000000000000.

$$1.6003345290410507=\frac{2108618102905538}{445690948547231}$$

Convert decimal number 1.6003345290410507 to fraction \frac{16003345290410507}{10000000000}. Reduce the fraction \frac{16003345290410507}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{16003345290410507}{10000000000000000}=\frac{2108618102905538}{445690948547231}$$

Least common multiple of 10000000000000000 and 445690948547231 is 4456909485472310000000000000000. Convert \frac{16003345290410507}{10000000000000000} and \frac{2108618102905538}{445690948547231} to fractions with denominator 4456909485472310000000000000000.

$$\frac{7132546142411920820607268156117}{4456909485472310000000000000000}=\frac{21086181029055380000000000000000}{4456909485472310000000000000000}$$

Compare \frac{7132546142411920820607268156117}{4456909485472310000000000000000} and \frac{21086181029055380000000000000000}{4456909485472310000000000000000}.

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