Solve 2sin(54)*cos(18)+cos(18)divcos(36)

$$2 \sin ( 54 ) \times \cos ( 18 ) + \cos ( 18 ) \div \cos ( 36 )$$

Evaluate

$$\frac{351360905397847004142123153406350739683825387}{129442719099991600000000000000000000000000000}\approx 2.714412273$$

Solution Steps

Evaluate trigonometric functions in the problem

$$2 \cdot 0.8090169943749475 \cdot 0.9510565162951535 + 0.9510565162951535 / 0.8090169943749475$$

Multiply 2 and 0.8090169943749475 to get 1.618033988749895.

$$1.618033988749895\times 0.9510565162951535+\frac{0.9510565162951535}{0.8090169943749475}$$

Multiply 1.618033988749895 and 0.9510565162951535 to get 1.5388417685876267289643121338825.

$$1.5388417685876267289643121338825+\frac{0.9510565162951535}{0.8090169943749475}$$

Expand \frac{0.9510565162951535}{0.8090169943749475} by multiplying both numerator and the denominator by 10000000000000000.

$$1.5388417685876267289643121338825+\frac{9510565162951535}{8090169943749475}$$

Reduce the fraction \frac{9510565162951535}{8090169943749475} to lowest terms by extracting and canceling out 5.

$$1.5388417685876267289643121338825+\frac{1902113032590307}{1618033988749895}$$

Convert decimal number 1.5388417685876267289643121338825 to fraction \frac{615536707435050691585724853553}{10000000000}. Reduce the fraction \frac{615536707435050691585724853553}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{615536707435050691585724853553}{400000000000000000000000000000}+\frac{1902113032590307}{1618033988749895}$$

Least common multiple of 400000000000000000000000000000 and 1618033988749895 is 129442719099991600000000000000000000000000000. Convert \frac{615536707435050691585724853553}{400000000000000000000000000000} and \frac{1902113032590307}{1618033988749895} to fractions with denominator 129442719099991600000000000000000000000000000.

$$\frac{199191862790622444142123153406350739683825387}{129442719099991600000000000000000000000000000}+\frac{152169042607224560000000000000000000000000000}{129442719099991600000000000000000000000000000}$$

Since \frac{199191862790622444142123153406350739683825387}{129442719099991600000000000000000000000000000} and \frac{152169042607224560000000000000000000000000000}{129442719099991600000000000000000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{199191862790622444142123153406350739683825387+152169042607224560000000000000000000000000000}{129442719099991600000000000000000000000000000}$$

Add 199191862790622444142123153406350739683825387 and 152169042607224560000000000000000000000000000 to get 351360905397847004142123153406350739683825387.

$$\frac{351360905397847004142123153406350739683825387}{129442719099991600000000000000000000000000000}$$