Leysa (2)3/sin^{220^{circ}}-1/cos^220^circ+64sin^220^circ

$$( 2 ) \frac { 3 } { \sin ^ { 2 } 20 ^ { \circ } } - \frac { 1 } { \cos ^ { 2 } 20 ^ { \circ } } + 64 \sin ^ { 2 } 20 ^ { \circ }$$

Meta

$$\frac{5814915970713618737501269924237505759233698368644990171879009323293911055544430132267890353801}{100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000}\approx 57.645896511$$

Lausnarskref

Evaluate trigonometric functions in the problem

$${(2)} \frac{3}{0.3420201433256687 ^ {2}} - \frac{1}{0.9396926207859084 ^ {2}} + 64 \cdot 0.3420201433256687 ^ {2}$$

Reiknaðu 0.3420201433256687 í 2. veldi og fáðu 0.11697777844051095979530830215969.

$$2\times \frac{3}{0.11697777844051095979530830215969}-\frac{1}{0.9396926207859084^{2}}+64\times 0.3420201433256687^{2}$$

Leystu upp \frac{3}{0.11697777844051095979530830215969} með því að margfalda bæði teljara og nefnara með 100000000000000000000000000000000.

$$2\times \frac{300000000000000000000000000000000}{11697777844051095979530830215969}-\frac{1}{0.9396926207859084^{2}}+64\times 0.3420201433256687^{2}$$

Sýndu 2\times \frac{300000000000000000000000000000000}{11697777844051095979530830215969} sem eitt brot.

$$\frac{2\times 300000000000000000000000000000000}{11697777844051095979530830215969}-\frac{1}{0.9396926207859084^{2}}+64\times 0.3420201433256687^{2}$$

Margfaldaðu 2 og 300000000000000000000000000000000 til að fá út 600000000000000000000000000000000.

$$\frac{600000000000000000000000000000000}{11697777844051095979530830215969}-\frac{1}{0.9396926207859084^{2}}+64\times 0.3420201433256687^{2}$$

Reiknaðu 0.9396926207859084 í 2. veldi og fáðu 0.88302222155948904756966801319056.

$$\frac{600000000000000000000000000000000}{11697777844051095979530830215969}-\frac{1}{0.88302222155948904756966801319056}+64\times 0.3420201433256687^{2}$$

Leystu upp \frac{1}{0.88302222155948904756966801319056} með því að margfalda bæði teljara og nefnara með 100000000000000000000000000000000.

$$\frac{600000000000000000000000000000000}{11697777844051095979530830215969}-\frac{100000000000000000000000000000000}{88302222155948904756966801319056}+64\times 0.3420201433256687^{2}$$

Minnka brotið \frac{100000000000000000000000000000000}{88302222155948904756966801319056} eins mikið og hægt er með því að draga og stytta út 16.

$$\frac{600000000000000000000000000000000}{11697777844051095979530830215969}-\frac{6250000000000000000000000000000}{5518888884746806547310425082441}+64\times 0.3420201433256687^{2}$$

Sjaldgæfasta margfeldi 11697777844051095979530830215969 og 5518888884746806547310425082441 er 64558736119771056212369977545857700093089334767336350659700329. Breyttu \frac{600000000000000000000000000000000}{11697777844051095979530830215969} og \frac{6250000000000000000000000000000}{5518888884746806547310425082441} í brot með nefnaranum 64558736119771056212369977545857700093089334767336350659700329.

$$\frac{3311333330848083928386255049464600000000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329}-\frac{73111111525319349872067688849806250000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329}+64\times 0.3420201433256687^{2}$$

Þar sem \frac{3311333330848083928386255049464600000000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329} og \frac{73111111525319349872067688849806250000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329} eru með sama nefnara skaltu draga frá með því að nota frádrátt á teljarana.

$$\frac{3311333330848083928386255049464600000000000000000000000000000000-73111111525319349872067688849806250000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329}+64\times 0.3420201433256687^{2}$$

Dragðu 73111111525319349872067688849806250000000000000000000000000000 frá 3311333330848083928386255049464600000000000000000000000000000000 til að fá út 3238222219322764578514187360614793750000000000000000000000000000.

$$\frac{3238222219322764578514187360614793750000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329}+64\times 0.3420201433256687^{2}$$

Reiknaðu 0.3420201433256687 í 2. veldi og fáðu 0.11697777844051095979530830215969.

$$\frac{3238222219322764578514187360614793750000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329}+64\times 0.11697777844051095979530830215969$$

Margfaldaðu 64 og 0.11697777844051095979530830215969 til að fá út 7.48657782019270142689973133822016.

$$\frac{3238222219322764578514187360614793750000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329}+7.48657782019270142689973133822016$$

Breyta tugabrotinu 7.48657782019270142689973133822016 í brot \frac{11697777844051095979530830215969}{10000000000}. Minnka brotið \frac{11697777844051095979530830215969}{10000000000} eins mikið og hægt er með því að draga og stytta út 1.

$$\frac{3238222219322764578514187360614793750000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329}+\frac{11697777844051095979530830215969}{1562500000000000000000000000000}$$

Sjaldgæfasta margfeldi 64558736119771056212369977545857700093089334767336350659700329 og 1562500000000000000000000000000 er 100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000. Breyttu \frac{3238222219322764578514187360614793750000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329} og \frac{11697777844051095979530830215969}{1562500000000000000000000000000} í brot með nefnaranum 100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000.

$$\frac{5059722217691819653928417750960615234375000000000000000000000000000000000000000000000000000000}{100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000}+\frac{755193753021799083572852173276890524858698368644990171879009323293911055544430132267890353801}{100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000}$$

Þar sem \frac{5059722217691819653928417750960615234375000000000000000000000000000000000000000000000000000000}{100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000} og \frac{755193753021799083572852173276890524858698368644990171879009323293911055544430132267890353801}{100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000} eru með sama nefnara skaltu leggja saman með því að leggja saman teljarana.

$$\frac{5059722217691819653928417750960615234375000000000000000000000000000000000000000000000000000000+755193753021799083572852173276890524858698368644990171879009323293911055544430132267890353801}{100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000}$$

Leggðu saman 5059722217691819653928417750960615234375000000000000000000000000000000000000000000000000000000 og 755193753021799083572852173276890524858698368644990171879009323293911055544430132267890353801 til að fá 5814915970713618737501269924237505759233698368644990171879009323293911055544430132267890353801.

$$\frac{5814915970713618737501269924237505759233698368644990171879009323293911055544430132267890353801}{100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000}$$