Solve sin15^circ/sin5^circ-cos15^circ/cos5^circ

$$\frac { \sin 15 ^ { \circ } } { \sin 5 ^ { \circ } } - \frac { \cos 15 ^ { \circ } } { \cos 5 ^ { \circ } }$$

Evaluate

$$\frac{57882725888976773503762846789553}{28941362944488389355545977545245}\approx 2$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.25881904510252074}{0.08715574274765817} - \frac{0.9659258262890683}{0.9961946980917455}$$

Expand \frac{0.25881904510252074}{0.08715574274765817} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{25881904510252074}{8715574274765817}-\frac{0.9659258262890683}{0.9961946980917455}$$

Reduce the fraction \frac{25881904510252074}{8715574274765817} to lowest terms by extracting and canceling out 3.

$$\frac{8627301503417358}{2905191424921939}-\frac{0.9659258262890683}{0.9961946980917455}$$

Expand \frac{0.9659258262890683}{0.9961946980917455} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{8627301503417358}{2905191424921939}-\frac{9659258262890683}{9961946980917455}$$

Least common multiple of 2905191424921939 and 9961946980917455 is 28941362944488389355545977545245. Convert \frac{8627301503417358}{2905191424921939} and \frac{9659258262890683}{9961946980917455} to fractions with denominator 28941362944488389355545977545245.

$$\frac{85944720165433170108496612183890}{28941362944488389355545977545245}-\frac{28061994276456396604733765394337}{28941362944488389355545977545245}$$

Since \frac{85944720165433170108496612183890}{28941362944488389355545977545245} and \frac{28061994276456396604733765394337}{28941362944488389355545977545245} have the same denominator, subtract them by subtracting their numerators.

$$\frac{85944720165433170108496612183890-28061994276456396604733765394337}{28941362944488389355545977545245}$$

Subtract 28061994276456396604733765394337 from 85944720165433170108496612183890 to get 57882725888976773503762846789553.

$$\frac{57882725888976773503762846789553}{28941362944488389355545977545245}$$

Factor

$$\frac{7 \cdot 3833 \cdot 5479 \cdot 87839096357 \cdot 4482527434421}{5 \cdot 271 \cdot 499 \cdot 12503 \cdot 1178393 \cdot 2905191424921939} = 1\frac{2.8941362944488387 \times 10^{31}}{2.8941362944488396 \times 10^{31}} = 1.9999999999999998$$