Solve 1-sin^210^circ/cos^280^circ

$$\frac { 1 - \sin ^ { 2 } 10 ^ { \circ } } { \cos ^ { 2 } 80 ^ { \circ } }$$

Evaluate

$$\frac{9698463103929541985741871149260911}{301536896070458292095213117827681}\approx 32.163437478$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1 - 0.17364817766693033 ^ {2}}{0.17364817766693041 ^ {2}}$$

Calculate 0.17364817766693033 to the power of 2 and get 0.0301536896070458014258128850739089.

$$\frac{1-0.0301536896070458014258128850739089}{0.17364817766693041^{2}}$$

Subtract 0.0301536896070458014258128850739089 from 1 to get 0.9698463103929541985741871149260911.

$$\frac{0.9698463103929541985741871149260911}{0.17364817766693041^{2}}$$

Calculate 0.17364817766693041 to the power of 2 and get 0.0301536896070458292095213117827681.

$$\frac{0.9698463103929541985741871149260911}{0.0301536896070458292095213117827681}$$

Expand \frac{0.9698463103929541985741871149260911}{0.0301536896070458292095213117827681} by multiplying both numerator and the denominator by 10000000000000000000000000000000000.

$$\frac{9698463103929541985741871149260911}{301536896070458292095213117827681}$$