Solve cos37sec12/cos12

$$\frac { \cos 37 \sec 12 } { \cos 12 }$$

Evaluate

$$\frac{850497398356338964015912351749}{1018903750764380937500000000000}\approx 0.834718096$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.7986355100472928 \cdot 1.0223405948650293}{0.9781476007338057}$$

Multiply 0.7986355100472928 and 1.0223405948650293 to get 0.81647750242208540545527585767904.

$$\frac{0.81647750242208540545527585767904}{0.9781476007338057}$$

Expand \frac{0.81647750242208540545527585767904}{0.9781476007338057} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$\frac{81647750242208540545527585767904}{97814760073380570000000000000000}$$

Reduce the fraction \frac{81647750242208540545527585767904}{97814760073380570000000000000000} to lowest terms by extracting and canceling out 96.

$$\frac{850497398356338964015912351749}{1018903750764380937500000000000}$$

Factor

$$\frac{3 \cdot 79 \cdot 467 \cdot 563 \cdot 607 \cdot 145259 \cdot 3159159454301 \cdot 7 ^ {2}}{11 \cdot 17 \cdot 19 \cdot 101 \cdot 673 \cdot 13500551 \cdot 2 ^ {11} \cdot 5 ^ {16}} = 0.8347180955201081$$