Solve cos(99)/cos(33)-sin(99)/sin(33)

$$\frac{ \cos ( 99 ) }{ \cos ( 33 ) } - \frac{ \sin ( 99 ) }{ \sin ( 33 ) }$$

Evaluate

$$-\frac{14274147775665639690205403449156}{7137073887832819476834573140475}\approx -2$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{-0.15643446504023104}{0.838670567945424} - \frac{0.9876883405951377}{0.5446390350150271}$$

Expand \frac{-0.15643446504023104}{0.838670567945424} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{-15643446504023104}{83867056794542400}-\frac{0.9876883405951377}{0.5446390350150271}$$

Reduce the fraction \frac{-15643446504023104}{83867056794542400} to lowest terms by extracting and canceling out 64.

$$-\frac{244428851625361}{1310422762414725}-\frac{0.9876883405951377}{0.5446390350150271}$$

Expand \frac{0.9876883405951377}{0.5446390350150271} by multiplying both numerator and the denominator by 10000000000000000.

$$-\frac{244428851625361}{1310422762414725}-\frac{9876883405951377}{5446390350150271}$$

Least common multiple of 1310422762414725 and 5446390350150271 is 7137073887832819476834573140475. Convert -\frac{244428851625361}{1310422762414725} and \frac{9876883405951377}{5446390350150271} to fractions with denominator 7137073887832819476834573140475.

$$-\frac{1331254938790678533628944622831}{7137073887832819476834573140475}-\frac{12942892836874961156576458826325}{7137073887832819476834573140475}$$

Since -\frac{1331254938790678533628944622831}{7137073887832819476834573140475} and \frac{12942892836874961156576458826325}{7137073887832819476834573140475} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1331254938790678533628944622831-12942892836874961156576458826325}{7137073887832819476834573140475}$$

Subtract 12942892836874961156576458826325 from -1331254938790678533628944622831 to get -14274147775665639690205403449156.

$$-\frac{14274147775665639690205403449156}{7137073887832819476834573140475}$$