Løs 1/sin^220^circ-tan^2110^circ

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

Evaluer

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

Løsningstrinn

Evaluate trigonometric functions in the problem

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

Regn ut 0,3420201433256687 opphøyd i 2 og få 0,11697777844051095979530830215969.

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

Utvid \frac{1}{0,11697777844051095979530830215969} ved å multiplisere både telleren og nevneren med 100000000000000000000000000000000.

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

Regn ut 2,7474774194546225 opphøyd i 2 og få 7,54863217041303166704533661750625.

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

Det motsatte av -7,54863217041303166704533661750625 er 7,54863217041303166704533661750625.

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

Konverter desimaltallet 7,54863217041303166704533661750625 til brøken \frac{1207781147266085066727253858801}{10000000000}. Forkort brøken \frac{1207781147266085066727253858801}{10000000000} til minste felles nevner ved å dele teller og nevner på 1.

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

Minste felles multiplum av 11697777844051095979530830215969 og 160000000000000000000000000000 er 1871644455048175356724932834555040000000000000000000000000000. Konverter \frac{100000000000000000000000000000000}{11697777844051095979530830215969} og \frac{1207781147266085066727253858801}{160000000000000000000000000000} til brøker med nevner 1871644455048175356724932834555040000000000000000000000000000.

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

Siden \frac{16000000000000000000000000000000000000000000000000000000000000}{1871644455048175356724932834555040000000000000000000000000000} og \frac{14128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000} har samme nevner, kan du legge dem sammen ved å legge sammen tellerne.

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

Legg sammen 16000000000000000000000000000000000000000000000000000000000000 og 14128355544951823826959762297674094096820918803064623461393169 for å få 30128355544951823826959762297674094096820918803064623461393169.

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