Solve 1/sin^220^circ-tan^2110^circ

$$\frac { 1 } { \sin ^ { 2 } 20 ^ { \circ } } - \tan ^ { 2 } 110 ^ { \circ }$$

Evaluate

$$\frac{30128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000}\approx 16.097264341$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1}{0.3420201433256687 ^ {2}} - -2.7474774194546225 ^ {2}$$

Calculate 0.3420201433256687 to the power of 2 and get 0.11697777844051095979530830215969.

$$\frac{1}{0.11697777844051095979530830215969}-\left(-2.7474774194546225^{2}\right)$$

Expand \frac{1}{0.11697777844051095979530830215969} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$\frac{100000000000000000000000000000000}{11697777844051095979530830215969}-\left(-2.7474774194546225^{2}\right)$$

Calculate 2.7474774194546225 to the power of 2 and get 7.54863217041303166704533661750625.

$$\frac{100000000000000000000000000000000}{11697777844051095979530830215969}-\left(-7.54863217041303166704533661750625\right)$$

The opposite of -7.54863217041303166704533661750625 is 7.54863217041303166704533661750625.

$$\frac{100000000000000000000000000000000}{11697777844051095979530830215969}+7.54863217041303166704533661750625$$

Convert decimal number 7.54863217041303166704533661750625 to fraction \frac{1207781147266085066727253858801}{10000000000}. Reduce the fraction \frac{1207781147266085066727253858801}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{100000000000000000000000000000000}{11697777844051095979530830215969}+\frac{1207781147266085066727253858801}{160000000000000000000000000000}$$

Least common multiple of 11697777844051095979530830215969 and 160000000000000000000000000000 is 1871644455048175356724932834555040000000000000000000000000000. Convert \frac{100000000000000000000000000000000}{11697777844051095979530830215969} and \frac{1207781147266085066727253858801}{160000000000000000000000000000} to fractions with denominator 1871644455048175356724932834555040000000000000000000000000000.

$$\frac{16000000000000000000000000000000000000000000000000000000000000}{1871644455048175356724932834555040000000000000000000000000000}+\frac{14128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000}$$

Since \frac{16000000000000000000000000000000000000000000000000000000000000}{1871644455048175356724932834555040000000000000000000000000000} and \frac{14128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{16000000000000000000000000000000000000000000000000000000000000+14128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000}$$

Add 16000000000000000000000000000000000000000000000000000000000000 and 14128355544951823826959762297674094096820918803064623461393169 to get 30128355544951823826959762297674094096820918803064623461393169.

$$\frac{30128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000}$$