Solve frac{sin15^{circ}cos15^circ}{15^circ-sin^215^circ}

$$\frac { \sin 15 ^ { \circ } \cos 15 ^ { \circ } } { 15 ^ { \circ } - \sin ^ { 2 } 15 ^ { \circ } }$$

Evaluate

$$\frac{208333333333333318201700196688785}{12444177251576849445792085748224877}\approx 0.016741431$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.25881904510252074 \cdot 0.9659258262890683}{15 - 0.25881904510252074 ^ {2}}$$

Multiply 0.25881904510252074 and 0.9659258262890683 to get 0.249999999999999981842040236026542.

$$\frac{0.249999999999999981842040236026542}{15-0.25881904510252074^{2}}$$

Calculate 0.25881904510252074 to the power of 2 and get 0.0669872981077806650494971021301476.

$$\frac{0.249999999999999981842040236026542}{15-0.0669872981077806650494971021301476}$$

Subtract 0.0669872981077806650494971021301476 from 15 to get 14.9330127018922193349505028978698524.

$$\frac{0.249999999999999981842040236026542}{14.9330127018922193349505028978698524}$$

Expand \frac{0.249999999999999981842040236026542}{14.9330127018922193349505028978698524} by multiplying both numerator and the denominator by 10000000000000000000000000000000000.

$$\frac{2499999999999999818420402360265420}{149330127018922193349505028978698524}$$

Reduce the fraction \frac{2499999999999999818420402360265420}{149330127018922193349505028978698524} to lowest terms by extracting and canceling out 12.

$$\frac{208333333333333318201700196688785}{12444177251576849445792085748224877}$$