Solve 2sinpi/12/cosfrac{pi{12}}-sinpi/6-2/frac{1{2}sinfrac{pi}{12}}

$$\frac { 2 \sin \frac { \pi } { 12 } } { \cos \frac { \pi } { 12 } } - \frac { \sin \frac { \pi } { 6 } - 2 } { \frac { 1 } { 2 } \sin \frac { \pi } { 12 } }$$

Evaluate

$$\frac{2526460062568971858415828503550246}{208333333333333318201700196688785}\approx 12.1270083$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{2 \cdot 0.25881904510252074}{0.9659258262890683} - \frac{\sin(\frac{\pi}{6}) - 2}{\frac{1}{2} 0.25881904510252074}$$

Multiply 2 and 0.25881904510252074 to get 0.51763809020504148.

$$\frac{0.51763809020504148}{0.9659258262890683}-\frac{\sin(\frac{\pi }{6})-2}{\frac{1}{2}\times 0.25881904510252074}$$

Expand \frac{0.51763809020504148}{0.9659258262890683} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{51763809020504148}{96592582628906830}-\frac{\sin(\frac{\pi }{6})-2}{\frac{1}{2}\times 0.25881904510252074}$$

Reduce the fraction \frac{51763809020504148}{96592582628906830} to lowest terms by extracting and canceling out 2.

$$\frac{25881904510252074}{48296291314453415}-\frac{\sin(\frac{\pi }{6})-2}{\frac{1}{2}\times 0.25881904510252074}$$

Get the value of \sin(\frac{\pi }{6}) from trigonometric values table.

$$\frac{25881904510252074}{48296291314453415}-\frac{\frac{1}{2}-2}{\frac{1}{2}\times 0.25881904510252074}$$

Subtract 2 from \frac{1}{2} to get -\frac{3}{2}.

$$\frac{25881904510252074}{48296291314453415}-\frac{-\frac{3}{2}}{\frac{1}{2}\times 0.25881904510252074}$$

Multiply \frac{1}{2} and 0.25881904510252074 to get \frac{12940952255126037}{100000000000000000}.

$$\frac{25881904510252074}{48296291314453415}-\frac{-\frac{3}{2}}{\frac{12940952255126037}{100000000000000000}}$$

Divide -\frac{3}{2} by \frac{12940952255126037}{100000000000000000} by multiplying -\frac{3}{2} by the reciprocal of \frac{12940952255126037}{100000000000000000}.

$$\frac{25881904510252074}{48296291314453415}-\left(-\frac{3}{2}\times \frac{100000000000000000}{12940952255126037}\right)$$

Multiply -\frac{3}{2} and \frac{100000000000000000}{12940952255126037} to get -\frac{50000000000000000}{4313650751708679}.

$$\frac{25881904510252074}{48296291314453415}-\left(-\frac{50000000000000000}{4313650751708679}\right)$$

The opposite of -\frac{50000000000000000}{4313650751708679} is \frac{50000000000000000}{4313650751708679}.

$$\frac{25881904510252074}{48296291314453415}+\frac{50000000000000000}{4313650751708679}$$

Add \frac{25881904510252074}{48296291314453415} and \frac{50000000000000000}{4313650751708679} to get \frac{2526460062568971858415828503550246}{208333333333333318201700196688785}.

$$\frac{2526460062568971858415828503550246}{208333333333333318201700196688785}$$