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

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

Laske

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

Ratkaisun vaiheet

Evaluate trigonometric functions in the problem

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

Laske 0,3420201433256687 potenssiin 2, jolloin ratkaisuksi tulee 0,11697777844051095979530830215969.

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

Lavenna \frac{1}{0,11697777844051095979530830215969} kertomalla sekä osoittaja että nimittäjä luvulla 100000000000000000000000000000000.

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

Laske 2,7474774194546225 potenssiin 2, jolloin ratkaisuksi tulee 7,54863217041303166704533661750625.

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

Luvun -7,54863217041303166704533661750625 vastaluku on 7,54863217041303166704533661750625.

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

Muunna desimaaliluku 7,54863217041303166704533661750625 murtoluvuksi \frac{1207781147266085066727253858801}{10000000000}. Supista murtoluku \frac{1207781147266085066727253858801}{10000000000} luvulla 1.

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

Lukujen 11697777844051095979530830215969 ja 160000000000000000000000000000 pienin yhteinen jaettava on 1871644455048175356724932834555040000000000000000000000000000. Muunna \frac{100000000000000000000000000000000}{11697777844051095979530830215969} ja \frac{1207781147266085066727253858801}{160000000000000000000000000000} murtoluvuiksi, joiden nimittäjä on 1871644455048175356724932834555040000000000000000000000000000.

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

Koska arvoilla \frac{16000000000000000000000000000000000000000000000000000000000000}{1871644455048175356724932834555040000000000000000000000000000} ja \frac{14128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000} on sama nimittäjä, laske ne yhteen laskemalla niiden osoittajat yhteen.

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

Selvitä 30128355544951823826959762297674094096820918803064623461393169 laskemalla yhteen 16000000000000000000000000000000000000000000000000000000000000 ja 14128355544951823826959762297674094096820918803064623461393169.

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