Solve 3cos(43)/sin(47)-cos(37)csc(53)/tan(5)tan(25)tan(45)tan(65)tan(25)

$$\frac{ 3 \cos ( 43 ) }{ \sin ( 47 ) } - \frac{ \cos ( 37 ) \csc ( 53 ) }{ \tan ( 5 ) \tan ( 25 ) \tan ( 45 ) \tan ( 65 ) \tan ( 25 ) }$$

Evaluate

$$-\frac{26743474757539702023793352413346860900972019953057676205921731640774349894181158}{1243198714419689157399093653083346015529222667447893232502047586967097443313395}\approx -21.511826265$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{3 \cdot 0.7313537016191706}{0.7313537016191705} - \frac{0.7986355100472928 \cdot 1.2521356581562257}{0.08748866352592401 \cdot 0.4663076581549986 \tan(45) 2.1445069205095586 \cdot 0.4663076581549986}$$

Multiply 3 and 0.7313537016191706 to get 2.1940611048575118.

$$\frac{2.1940611048575118}{0.7313537016191705}-\frac{0.7986355100472928\times 1.2521356581562257}{0.08748866352592401\times 0.4663076581549986\times 0.4663076581549986\times 2.1445069205095586\tan(45)}$$

Expand \frac{2.1940611048575118}{0.7313537016191705} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{21940611048575118}{7313537016191705}-\frac{0.7986355100472928\times 1.2521356581562257}{0.08748866352592401\times 0.4663076581549986\times 0.4663076581549986\times 2.1445069205095586\tan(45)}$$

Multiply 0.7986355100472928 and 1.2521356581562257 to get 0.99999999999999997284865775078496.

$$\frac{21940611048575118}{7313537016191705}-\frac{0.99999999999999997284865775078496}{0.08748866352592401\times 0.4663076581549986\times 0.4663076581549986\times 2.1445069205095586\tan(45)}$$

Multiply 0.08748866352592401 and 0.4663076581549986 to get 0.040796633803884267751457865256386.

$$\frac{21940611048575118}{7313537016191705}-\frac{0.99999999999999997284865775078496}{0.040796633803884267751457865256386\times 0.4663076581549986\times 2.1445069205095586\tan(45)}$$

Multiply 0.040796633803884267751457865256386 and 0.4663076581549986 to get 0.0190237827696963253225419792968860422777164710596.

$$\frac{21940611048575118}{7313537016191705}-\frac{0.99999999999999997284865775078496}{0.0190237827696963253225419792968860422777164710596\times 2.1445069205095586\tan(45)}$$

Multiply 0.0190237827696963253225419792968860422777164710596 and 2.1445069205095586 to get 0.04079663380388426806759308854916789152772577004786594862207029256.

$$\frac{21940611048575118}{7313537016191705}-\frac{0.99999999999999997284865775078496}{0.04079663380388426806759308854916789152772577004786594862207029256\tan(45)}$$

Get the value of \tan(45) from trigonometric values table.

$$\frac{21940611048575118}{7313537016191705}-\frac{0.99999999999999997284865775078496}{0.04079663380388426806759308854916789152772577004786594862207029256\times 1}$$

Multiply 0.04079663380388426806759308854916789152772577004786594862207029256 and 1 to get 0.04079663380388426806759308854916789152772577004786594862207029256.

$$\frac{21940611048575118}{7313537016191705}-\frac{0.99999999999999997284865775078496}{0.04079663380388426806759308854916789152772577004786594862207029256}$$

Expand \frac{0.99999999999999997284865775078496}{0.04079663380388426806759308854916789152772577004786594862207029256} by multiplying both numerator and the denominator by 100000000000000000000000000000000000000000000000000000000000000000.

$$\frac{21940611048575118}{7313537016191705}-\frac{99999999999999997284865775078496000000000000000000000000000000000}{4079663380388426806759308854916789152772577004786594862207029256}$$

Reduce the fraction \frac{99999999999999997284865775078496000000000000000000000000000000000}{4079663380388426806759308854916789152772577004786594862207029256} to lowest terms by extracting and canceling out 24.

$$\frac{21940611048575118}{7313537016191705}-\frac{4166666666666666553536073961604000000000000000000000000000000000}{169985974182851116948304535621532881365524041866108119258626219}$$

Subtract \frac{4166666666666666553536073961604000000000000000000000000000000000}{169985974182851116948304535621532881365524041866108119258626219} from \frac{21940611048575118}{7313537016191705} to get -\frac{26743474757539702023793352413346860900972019953057676205921731640774349894181158}{1243198714419689157399093653083346015529222667447893232502047586967097443313395}.

$$-\frac{26743474757539702023793352413346860900972019953057676205921731640774349894181158}{1243198714419689157399093653083346015529222667447893232502047586967097443313395}$$