Solve 3-sin(70^circ)/2-cos(10^circ)*cos(10^circ)

$$\frac{ 3- \sin ( 70 ^ { \circ } ) }{ 2- \cos ( 10 ^ { \circ } ) \times \cos ( 10 ^ { \circ } ) }$$

Evaluate

$$\frac{8048075700055045703125000000}{4024037850027523144150792831}\approx 2$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{3 - 0.9396926207859083}{2 - 0.984807753012208 \cdot 0.984807753012208}$$

Subtract 0.9396926207859083 from 3 to get 2.0603073792140917.

$$\frac{2.0603073792140917}{2-0.984807753012208\times 0.984807753012208}$$

Multiply 0.984807753012208 and 0.984807753012208 to get 0.969846310392954075097397035264.

$$\frac{2.0603073792140917}{2-0.969846310392954075097397035264}$$

Subtract 0.969846310392954075097397035264 from 2 to get 1.030153689607045924902602964736.

$$\frac{2.0603073792140917}{1.030153689607045924902602964736}$$

Expand \frac{2.0603073792140917}{1.030153689607045924902602964736} by multiplying both numerator and the denominator by 1000000000000000000000000000000.

$$\frac{2060307379214091700000000000000}{1030153689607045924902602964736}$$

Reduce the fraction \frac{2060307379214091700000000000000}{1030153689607045924902602964736} to lowest terms by extracting and canceling out 256.

$$\frac{8048075700055045703125000000}{4024037850027523144150792831}$$

Factor

$$\frac{7 \cdot 11 \cdot 47 \cdot 6719 \cdot 847303097 \cdot 2 ^ {6} \cdot 5 ^ {14}}{4024037850027523144150792831} = 1\frac{4.024037850027522 \times 10^{27}}{4.024037850027523 \times 10^{27}} = 1.9999999999999998$$