Solve frac{cos(-288^{circ})cot72^circ}{tan(-162^circ)sin108^circ}-tan18^circ9

$$\frac { \cos ( - 288 ^ { \circ } ) \cot 72 ^ { \circ } } { \tan ( - 162 ^ { \circ } ) \sin 108 ^ { \circ } } - \tan 18 ^ { \circ } 9$$

Evaluate

$$\frac{16734284657185609925404727059051601045667708637}{25751416197912295912081414765060000000000000000}\approx 0.649839392$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.30901699437494723 \cdot 0.3249196962329064}{0.32491969623290645 \cdot 0.9510565162951536} - -0.32491969623290645$$

Multiply 0.30901699437494723 and 0.3249196962329064 to get 0.100405707943113599686331289529272.

$$\frac{0.100405707943113599686331289529272}{0.32491969623290645\times 0.9510565162951536}-\left(-0.32491969623290645\right)$$

Multiply 0.32491969623290645 and 0.9510565162951536 to get 0.30901699437494755094497697718072.

$$\frac{0.100405707943113599686331289529272}{0.30901699437494755094497697718072}-\left(-0.32491969623290645\right)$$

Expand \frac{0.100405707943113599686331289529272}{0.30901699437494755094497697718072} by multiplying both numerator and the denominator by 1000000000000000000000000000000000.

$$\frac{100405707943113599686331289529272}{309016994374947550944976977180720}-\left(-0.32491969623290645\right)$$

Reduce the fraction \frac{100405707943113599686331289529272}{309016994374947550944976977180720} to lowest terms by extracting and canceling out 24.

$$\frac{4183571164296399986930470397053}{12875708098956147956040707382530}-\left(-0.32491969623290645\right)$$

The opposite of -0.32491969623290645 is 0.32491969623290645.

$$\frac{4183571164296399986930470397053}{12875708098956147956040707382530}+0.32491969623290645$$

Convert decimal number 0.32491969623290645 to fraction \frac{6498393924658129}{10000000000}. Reduce the fraction \frac{6498393924658129}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{4183571164296399986930470397053}{12875708098956147956040707382530}+\frac{6498393924658129}{20000000000000000}$$

Least common multiple of 12875708098956147956040707382530 and 20000000000000000 is 25751416197912295912081414765060000000000000000. Convert \frac{4183571164296399986930470397053}{12875708098956147956040707382530} and \frac{6498393924658129}{20000000000000000} to fractions with denominator 25751416197912295912081414765060000000000000000.

$$\frac{8367142328592799973860940794106000000000000000}{25751416197912295912081414765060000000000000000}+\frac{8367142328592809951543786264945601045667708637}{25751416197912295912081414765060000000000000000}$$

Since \frac{8367142328592799973860940794106000000000000000}{25751416197912295912081414765060000000000000000} and \frac{8367142328592809951543786264945601045667708637}{25751416197912295912081414765060000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{8367142328592799973860940794106000000000000000+8367142328592809951543786264945601045667708637}{25751416197912295912081414765060000000000000000}$$

Add 8367142328592799973860940794106000000000000000 and 8367142328592809951543786264945601045667708637 to get 16734284657185609925404727059051601045667708637.

$$\frac{16734284657185609925404727059051601045667708637}{25751416197912295912081414765060000000000000000}$$