Solve tan15^{circ}=sin15^circ/cos15^circ=sin30^circ/2/cosfrac{30^circ{2}}

$$\tan 15 ^ { \circ } = \frac { \sin 15 ^ { \circ } } { \cos 15 ^ { \circ } } = \frac { \sin \frac { 30 ^ { \circ } } { 2 } } { \cos \frac { 30 ^ { \circ } } { 2 } }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$0.2679491924311227 = \frac{0.25881904510252074}{0.9659258262890683} = \frac{0.25881904510252074}{0.9659258262890683}$$

Expand \frac{0.25881904510252074}{0.9659258262890683} by multiplying both numerator and the denominator by 100000000000000000.

$$0.2679491924311227=\frac{25881904510252074}{96592582628906830}\text{ and }\frac{0.25881904510252074}{0.9659258262890683}=\frac{0.25881904510252074}{0.9659258262890683}$$

Reduce the fraction \frac{25881904510252074}{96592582628906830} to lowest terms by extracting and canceling out 2.

$$0.2679491924311227=\frac{12940952255126037}{48296291314453415}\text{ and }\frac{0.25881904510252074}{0.9659258262890683}=\frac{0.25881904510252074}{0.9659258262890683}$$

Convert decimal number 0.2679491924311227 to fraction \frac{2679491924311227}{10000000000}. Reduce the fraction \frac{2679491924311227}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{2679491924311227}{10000000000000000}=\frac{12940952255126037}{48296291314453415}\text{ and }\frac{0.25881904510252074}{0.9659258262890683}=\frac{0.25881904510252074}{0.9659258262890683}$$

Least common multiple of 10000000000000000 and 48296291314453415 is 96592582628906830000000000000000. Convert \frac{2679491924311227}{10000000000000000} and \frac{12940952255126037}{48296291314453415} to fractions with denominator 96592582628906830000000000000000.

$$\frac{25881904510252075964728770598041}{96592582628906830000000000000000}=\frac{25881904510252074000000000000000}{96592582628906830000000000000000}\text{ and }\frac{0.25881904510252074}{0.9659258262890683}=\frac{0.25881904510252074}{0.9659258262890683}$$

Compare \frac{25881904510252075964728770598041}{96592582628906830000000000000000} and \frac{25881904510252074000000000000000}{96592582628906830000000000000000}.

$$\text{false}\text{ and }\frac{0.25881904510252074}{0.9659258262890683}=\frac{0.25881904510252074}{0.9659258262890683}$$

Expand \frac{0.25881904510252074}{0.9659258262890683} by multiplying both numerator and the denominator by 100000000000000000.

$$\text{false}\text{ and }\frac{25881904510252074}{96592582628906830}=\frac{0.25881904510252074}{0.9659258262890683}$$

Reduce the fraction \frac{25881904510252074}{96592582628906830} to lowest terms by extracting and canceling out 2.

$$\text{false}\text{ and }\frac{12940952255126037}{48296291314453415}=\frac{0.25881904510252074}{0.9659258262890683}$$

Expand \frac{0.25881904510252074}{0.9659258262890683} by multiplying both numerator and the denominator by 100000000000000000.

$$\text{false}\text{ and }\frac{12940952255126037}{48296291314453415}=\frac{25881904510252074}{96592582628906830}$$

Reduce the fraction \frac{25881904510252074}{96592582628906830} to lowest terms by extracting and canceling out 2.

$$\text{false}\text{ and }\frac{12940952255126037}{48296291314453415}=\frac{12940952255126037}{48296291314453415}$$

Compare \frac{12940952255126037}{48296291314453415} and \frac{12940952255126037}{48296291314453415}.

$$\text{false}\text{ and }\text{true}$$

The conjunction of \text{false} and \text{true} is \text{false}.

$$\text{false}$$