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

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

Vlerëso

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

Hapat e zgjidhjes

Evaluate trigonometric functions in the problem

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

Llogarit 0.3420201433256687 në fuqi të 2 dhe merr 0.11697777844051095979530830215969.

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

Zhvillo \frac{3}{0.11697777844051095979530830215969} duke shumëzuar si numëruesin ashtu dhe emëruesin me 100000000000000000000000000000000.

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

Shpreh 2\times \frac{300000000000000000000000000000000}{11697777844051095979530830215969} si një thyesë të vetme.

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

Shumëzo 2 me 300000000000000000000000000000000 për të marrë 600000000000000000000000000000000.

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

Llogarit 0.9396926207859084 në fuqi të 2 dhe merr 0.88302222155948904756966801319056.

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

Zhvillo \frac{1}{0.88302222155948904756966801319056} duke shumëzuar si numëruesin ashtu dhe emëruesin me 100000000000000000000000000000000.

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

Thjeshto thyesën \frac{100000000000000000000000000000000}{88302222155948904756966801319056} në kufizat më të vogla duke zbritur dhe thjeshtuar 16.

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

Shumëfishi më i vogël i përbashkët i 11697777844051095979530830215969 dhe 5518888884746806547310425082441 është 64558736119771056212369977545857700093089334767336350659700329. Konverto \frac{600000000000000000000000000000000}{11697777844051095979530830215969} dhe \frac{6250000000000000000000000000000}{5518888884746806547310425082441} në thyesa me emërues 64558736119771056212369977545857700093089334767336350659700329.

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

Meqenëse \frac{3311333330848083928386255049464600000000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329} dhe \frac{73111111525319349872067688849806250000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329} kanë të njëjtin emërues, zbriti duke zbritur numëruesit e tyre.

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

Zbrit 73111111525319349872067688849806250000000000000000000000000000 nga 3311333330848083928386255049464600000000000000000000000000000000 për të marrë 3238222219322764578514187360614793750000000000000000000000000000.

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

Llogarit 0.3420201433256687 në fuqi të 2 dhe merr 0.11697777844051095979530830215969.

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

Shumëzo 64 me 0.11697777844051095979530830215969 për të marrë 7.48657782019270142689973133822016.

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

Konverto numrin dhjetor 7.48657782019270142689973133822016 në thyesën \frac{11697777844051095979530830215969}{10000000000}. Thjeshto thyesën \frac{11697777844051095979530830215969}{10000000000} në kufizat më të vogla duke zbritur dhe thjeshtuar 1.

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

Shumëfishi më i vogël i përbashkët i 64558736119771056212369977545857700093089334767336350659700329 dhe 1562500000000000000000000000000 është 100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000. Konverto \frac{3238222219322764578514187360614793750000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329} dhe \frac{11697777844051095979530830215969}{1562500000000000000000000000000} në thyesa me emërues 100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000.

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

Meqenëse \frac{5059722217691819653928417750960615234375000000000000000000000000000000000000000000000000000000}{100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000} dhe \frac{755193753021799083572852173276890524858698368644990171879009323293911055544430132267890353801}{100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000} kanë të njëjtin emërues, mblidhi duke mbledhur numëruesit e tyre.

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

Shto 5059722217691819653928417750960615234375000000000000000000000000000000000000000000000000000000 dhe 755193753021799083572852173276890524858698368644990171879009323293911055544430132267890353801 për të marrë 5814915970713618737501269924237505759233698368644990171879009323293911055544430132267890353801.

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