求解 cos(99)/cos(33)-sin(99)/sin(33)

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

求值

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

求解步骤

对题中的三角函数求值

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

将分子和分母同时乘以 100000000000000000 以展开 \frac{-0.15643446504023104}{0.838670567945424}。

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

通过求根和消去 64，将分数 \frac{-15643446504023104}{83867056794542400} 降低为最简分数。

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

将分子和分母同时乘以 10000000000000000 以展开 \frac{0.9876883405951377}{0.5446390350150271}。

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

1310422762414725 和 5446390350150271 的最小公倍数是 7137073887832819476834573140475。将 -\frac{244428851625361}{1310422762414725} 和 \frac{9876883405951377}{5446390350150271} 转换为带分母 7137073887832819476834573140475 的分数。

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

由于 -\frac{1331254938790678533628944622831}{7137073887832819476834573140475} 和 \frac{12942892836874961156576458826325}{7137073887832819476834573140475} 具有相同的分母，可通过分子相减来求差。

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

将 -1331254938790678533628944622831 减去 12942892836874961156576458826325，得到 -14274147775665639690205403449156。

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