Résoudre 1/sin^220^circ-tan^2110^circ

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

Évaluer

$$\frac{30128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000}\approx 16,097264341$$

Étapes de la solution

Évaluer les fonctions trigonométriques du problème

$$\frac{1}{0,3420201433256687 ^ {2}} - -2,7474774194546225 ^ {2}$$

Calculer 0,3420201433256687 à la puissance 2 et obtenir 0,11697777844051095979530830215969.

$$\frac{1}{0,11697777844051095979530830215969}-\left(-2,7474774194546225^{2}\right)$$

Développez \frac{1}{0,11697777844051095979530830215969} en multipliant le numérateur et le dénominateur par 100000000000000000000000000000000.

$$\frac{100000000000000000000000000000000}{11697777844051095979530830215969}-\left(-2,7474774194546225^{2}\right)$$

Calculer 2,7474774194546225 à la puissance 2 et obtenir 7,54863217041303166704533661750625.

$$\frac{100000000000000000000000000000000}{11697777844051095979530830215969}-\left(-7,54863217041303166704533661750625\right)$$

L’inverse de -7,54863217041303166704533661750625 est 7,54863217041303166704533661750625.

$$\frac{100000000000000000000000000000000}{11697777844051095979530830215969}+7,54863217041303166704533661750625$$

Convertir le nombre décimal 7,54863217041303166704533661750625 en fraction \frac{1207781147266085066727253858801}{10000000000}. Réduire la fraction \frac{1207781147266085066727253858801}{10000000000} au maximum en extrayant et en annulant 1.

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

Le plus petit dénominateur commun de 11697777844051095979530830215969 et 160000000000000000000000000000 est 1871644455048175356724932834555040000000000000000000000000000. Convertissez \frac{100000000000000000000000000000000}{11697777844051095979530830215969} et \frac{1207781147266085066727253858801}{160000000000000000000000000000} en fractions avec le dénominateur 1871644455048175356724932834555040000000000000000000000000000.

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

Étant donné que \frac{16000000000000000000000000000000000000000000000000000000000000}{1871644455048175356724932834555040000000000000000000000000000} et \frac{14128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000} ont un dénominateur commun, additionnez-les en additionnant leur numérateur.

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

Additionner 16000000000000000000000000000000000000000000000000000000000000 et 14128355544951823826959762297674094096820918803064623461393169 pour obtenir 30128355544951823826959762297674094096820918803064623461393169.

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