Solve frac{cot430^{circ}}{cos(-250^{circ})}+sin215^circ/tan575^circsin(-290^circ)cos145^circ=

$$\frac { \cot 430 ^ { \circ } } { \cos ( - 250 ^ { \circ } ) } + \frac { \sin 215 ^ { \circ } } { \tan 575 ^ { \circ } \sin ( - 290 ^ { \circ } ) \cos 145 ^ { \circ } } =$$

Evaluate

$$\frac{19924134695377560823878090674027326752506878807}{15361992770608843016671351001507146531531192520668318557773574}\approx 1.296975919 \cdot 10^{-15}$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.3639702342662033}{-0.3420201433256694} + \frac{-0.5735764363510458}{0.7002075382097082 \cdot 0.9396926207859085 \cdot -0.8191520442889916}$$

Expand \frac{0.3639702342662033}{-0.3420201433256694} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{3639702342662033}{-3420201433256694}+\frac{-0.5735764363510458}{0.7002075382097082\times 0.9396926207859085\left(-0.8191520442889916\right)}$$

Fraction \frac{3639702342662033}{-3420201433256694} can be rewritten as -\frac{3639702342662033}{3420201433256694} by extracting the negative sign.

$$-\frac{3639702342662033}{3420201433256694}+\frac{-0.5735764363510458}{0.7002075382097082\times 0.9396926207859085\left(-0.8191520442889916\right)}$$

Multiply 0.7002075382097082 and 0.9396926207859085 to get 0.6579798566743298639365684568997.

$$-\frac{3639702342662033}{3420201433256694}+\frac{-0.5735764363510458}{0.6579798566743298639365684568997\left(-0.8191520442889916\right)}$$

Multiply 0.6579798566743298639365684568997 and -0.8191520442889916 to get -0.53898554469575500192196720412212637485577534252.

$$-\frac{3639702342662033}{3420201433256694}+\frac{-0.5735764363510458}{-0.53898554469575500192196720412212637485577534252}$$

Expand \frac{-0.5735764363510458}{-0.53898554469575500192196720412212637485577534252} by multiplying both numerator and the denominator by 100000000000000000000000000000000000000000000000.

$$-\frac{3639702342662033}{3420201433256694}+\frac{-57357643635104580000000000000000000000000000000}{-53898554469575500192196720412212637485577534252}$$

Reduce the fraction \frac{-57357643635104580000000000000000000000000000000}{-53898554469575500192196720412212637485577534252} to lowest terms by extracting and canceling out -12.

$$-\frac{3639702342662033}{3420201433256694}+\frac{4779803636258715000000000000000000000000000000}{4491546205797958349349726701017719790464794521}$$

Least common multiple of 3420201433256694 and 4491546205797958349349726701017719790464794521 is 15361992770608843016671351001507146531531192520668318557773574. Convert -\frac{3639702342662033}{3420201433256694} and \frac{4779803636258715000000000000000000000000000000}{4491546205797958349349726701017719790464794521} to fractions with denominator 15361992770608843016671351001507146531531192520668318557773574.

$$-\frac{16347891247417594792209694210649176121909325972673247493121193}{15361992770608843016671351001507146531531192520668318557773574}+\frac{16347891247417614716344389588210000000000000000000000000000000}{15361992770608843016671351001507146531531192520668318557773574}$$

Since -\frac{16347891247417594792209694210649176121909325972673247493121193}{15361992770608843016671351001507146531531192520668318557773574} and \frac{16347891247417614716344389588210000000000000000000000000000000}{15361992770608843016671351001507146531531192520668318557773574} have the same denominator, add them by adding their numerators.

$$\frac{-16347891247417594792209694210649176121909325972673247493121193+16347891247417614716344389588210000000000000000000000000000000}{15361992770608843016671351001507146531531192520668318557773574}$$

Add -16347891247417594792209694210649176121909325972673247493121193 and 16347891247417614716344389588210000000000000000000000000000000 to get 19924134695377560823878090674027326752506878807.

$$\frac{19924134695377560823878090674027326752506878807}{15361992770608843016671351001507146531531192520668318557773574}$$