Solve frac{12cos48^{circ}}{cos^224^circ-sin^224^circ}

$$\frac { 12 \cos 48 ^ { \circ } } { \cos ^ { 2 } 24 ^ { \circ } - \sin ^ { 2 } 24 ^ { \circ } }$$

Evaluate

$$\frac{214121794034834624000000000000000}{17843482836236220507349865438421}\approx 12$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{12 \cdot 0.6691306063588582}{0.9135454576426009 ^ {2} - 0.40673664307580015 ^ {2}}$$

Multiply 12 and 0.6691306063588582 to get 8.0295672763062984.

$$\frac{8.0295672763062984}{0.9135454576426009^{2}-0.40673664307580015^{2}}$$

Calculate 0.9135454576426009 to the power of 2 and get 0.83456530317942911513115851668081.

$$\frac{8.0295672763062984}{0.83456530317942911513115851668081-0.40673664307580015^{2}}$$

Calculate 0.40673664307580015 to the power of 2 and get 0.1654346968205708461055385627400225.

$$\frac{8.0295672763062984}{0.83456530317942911513115851668081-0.1654346968205708461055385627400225}$$

Subtract 0.1654346968205708461055385627400225 from 0.83456530317942911513115851668081 to get 0.6691306063588582690256199539407875.

$$\frac{8.0295672763062984}{0.6691306063588582690256199539407875}$$

Expand \frac{8.0295672763062984}{0.6691306063588582690256199539407875} by multiplying both numerator and the denominator by 10000000000000000000000000000000000.

$$\frac{80295672763062984000000000000000000}{6691306063588582690256199539407875}$$

Reduce the fraction \frac{80295672763062984000000000000000000}{6691306063588582690256199539407875} to lowest terms by extracting and canceling out 375.

$$\frac{214121794034834624000000000000000}{17843482836236220507349865438421}$$

Factor

$$\frac{47 \cdot 757 \cdot 94034487529 \cdot 2 ^ {21} \cdot 5 ^ {15}}{3 \cdot 19 \cdot 31 \cdot 39485881 \cdot 51340763 \cdot 4981256746721} = 11\frac{1.7843482836236193 \times 10^{31}}{1.784348283623622 \times 10^{31}} = 11.999999999999998$$