Solve 3+4cos10^0+cos20^circ/4cos^45^0+3

$$\frac { 3 + 4 \cos 10 ^ { 0 } + \cos 20 ^ { \circ } } { 4 \cos ^ { 4 } 5 ^ { 0 } } + 3$$

Evaluate

$$\frac{2166497221621281225063744660751318006671272875966752584626937621}{434517791213924408354581553583772668890424291988917528208979207}\approx 4.985980472$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{3 + 4 \cdot 0.9998476951563913 + 0.9396926207859084}{4 \cdot 0.9998476951563913 ^ {4}} + 3$$

Multiply 4 and 0.9998476951563913 to get 3.9993907806255652.

$$\frac{3+3.9993907806255652+0.9396926207859084}{4\times 0.9998476951563913^{4}}+3$$

Add 3 and 3.9993907806255652 to get 6.9993907806255652.

$$\frac{6.9993907806255652+0.9396926207859084}{4\times 0.9998476951563913^{4}}+3$$

Add 6.9993907806255652 and 0.9396926207859084 to get 7.9390834014114736.

$$\frac{7.9390834014114736}{4\times 0.9998476951563913^{4}}+3$$

Calculate 0.9998476951563913 to the power of 4 and get 0.9993909197920261392155375732426771384479758715745103148806521761.

$$\frac{7.9390834014114736}{4\times 0.9993909197920261392155375732426771384479758715745103148806521761}+3$$

Multiply 4 and 0.9993909197920261392155375732426771384479758715745103148806521761 to get 3.9975636791681045568621502929707085537919034862980412595226087044.

$$\frac{7.9390834014114736}{3.9975636791681045568621502929707085537919034862980412595226087044}+3$$

Expand \frac{7.9390834014114736}{3.9975636791681045568621502929707085537919034862980412595226087044} by multiplying both numerator and the denominator by 10000000000000000000000000000000000000000000000000000000000000000.

$$\frac{79390834014114736000000000000000000000000000000000000000000000000}{39975636791681045568621502929707085537919034862980412595226087044}+3$$

Reduce the fraction \frac{79390834014114736000000000000000000000000000000000000000000000000}{39975636791681045568621502929707085537919034862980412595226087044} to lowest terms by extracting and canceling out 92.

$$\frac{862943847979508000000000000000000000000000000000000000000000000}{434517791213924408354581553583772668890424291988917528208979207}+3$$

Convert 3 to fraction \frac{1303553373641773225063744660751318006671272875966752584626937621}{434517791213924408354581553583772668890424291988917528208979207}.

$$\frac{862943847979508000000000000000000000000000000000000000000000000}{434517791213924408354581553583772668890424291988917528208979207}+\frac{1303553373641773225063744660751318006671272875966752584626937621}{434517791213924408354581553583772668890424291988917528208979207}$$

Since \frac{862943847979508000000000000000000000000000000000000000000000000}{434517791213924408354581553583772668890424291988917528208979207} and \frac{1303553373641773225063744660751318006671272875966752584626937621}{434517791213924408354581553583772668890424291988917528208979207} have the same denominator, add them by adding their numerators.

$$\frac{862943847979508000000000000000000000000000000000000000000000000+1303553373641773225063744660751318006671272875966752584626937621}{434517791213924408354581553583772668890424291988917528208979207}$$

Add 862943847979508000000000000000000000000000000000000000000000000 and 1303553373641773225063744660751318006671272875966752584626937621 to get 2166497221621281225063744660751318006671272875966752584626937621.

$$\frac{2166497221621281225063744660751318006671272875966752584626937621}{434517791213924408354581553583772668890424291988917528208979207}$$