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

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

Verify

Solution Steps

Evaluate trigonometric functions in the problem

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

Multiply 2 and 0.554309051452769 to get 1.108618102905538.

$$1.6003345290410507=\frac{1.108618102905538}{1-0.554309051452769^{2}}$$

Calculate 0.554309051452769 to the power of 2 and get 0.307258524522468510629437767361.

$$1.6003345290410507=\frac{1.108618102905538}{1-0.307258524522468510629437767361}$$

Subtract 0.307258524522468510629437767361 from 1 to get 0.692741475477531489370562232639.

$$1.6003345290410507=\frac{1.108618102905538}{0.692741475477531489370562232639}$$

Expand \frac{1.108618102905538}{0.692741475477531489370562232639} by multiplying both numerator and the denominator by 1000000000000000000000000000000.

$$1.6003345290410507=\frac{1108618102905538000000000000000}{692741475477531489370562232639}$$

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.

$$\frac{16003345290410507}{10000000000000000}=\frac{1108618102905538000000000000000}{692741475477531489370562232639}$$

Least common multiple of 10000000000000000 and 692741475477531489370562232639 is 6927414754775314893705622326390000000000000000. Convert \frac{16003345290410507}{10000000000000000} and \frac{1108618102905538000000000000000}{692741475477531489370562232639} to fractions with denominator 6927414754775314893705622326390000000000000000.

$$\frac{11086181029055379286118927189462266310743937973}{6927414754775314893705622326390000000000000000}=\frac{11086181029055380000000000000000000000000000000}{6927414754775314893705622326390000000000000000}$$

Compare \frac{11086181029055379286118927189462266310743937973}{6927414754775314893705622326390000000000000000} and \frac{11086181029055380000000000000000000000000000000}{6927414754775314893705622326390000000000000000}.

$$\text{false}$$