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

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

मूल्यांकन करें

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

हल करने वाले चरण

सवाल में त्रिकोणमितीय फ़ंक्शन का मूल्‍यांकन करें

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

2 की घात की 0.3420201433256687 से गणना करें और 0.11697777844051095979530830215969 प्राप्त करें.

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

अंश और हर दोनों 100000000000000000000000000000000 से गुणा करके \frac{3}{0.11697777844051095979530830215969} को विस्तृत करें.

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

2\times \frac{300000000000000000000000000000000}{11697777844051095979530830215969} को एकल भिन्न के रूप में व्यक्त करें.

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

600000000000000000000000000000000 प्राप्त करने के लिए 2 और 300000000000000000000000000000000 का गुणा करें.

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

2 की घात की 0.9396926207859084 से गणना करें और 0.88302222155948904756966801319056 प्राप्त करें.

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

अंश और हर दोनों 100000000000000000000000000000000 से गुणा करके \frac{1}{0.88302222155948904756966801319056} को विस्तृत करें.

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

16 को निकालकर और रद्द करके भिन्न \frac{100000000000000000000000000000000}{88302222155948904756966801319056} को न्यूनतम पदों तक कम करें.

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

11697777844051095979530830215969 और 5518888884746806547310425082441 का लघुत्तम समापवर्त्य 64558736119771056212369977545857700093089334767336350659700329 है. \frac{600000000000000000000000000000000}{11697777844051095979530830215969} और \frac{6250000000000000000000000000000}{5518888884746806547310425082441} को 64558736119771056212369977545857700093089334767336350659700329 हर वाले भिन्न में रूपांतरित करें.

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

चूँकि \frac{3311333330848083928386255049464600000000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329} और \frac{73111111525319349872067688849806250000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329} का एक ही भाजक है, इसलिए उनके भाजकों को घटाकर उन्हें घटाएँ.

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

3238222219322764578514187360614793750000000000000000000000000000 प्राप्त करने के लिए 73111111525319349872067688849806250000000000000000000000000000 में से 3311333330848083928386255049464600000000000000000000000000000000 घटाएं.

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

2 की घात की 0.3420201433256687 से गणना करें और 0.11697777844051095979530830215969 प्राप्त करें.

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

7.48657782019270142689973133822016 प्राप्त करने के लिए 64 और 0.11697777844051095979530830215969 का गुणा करें.

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

दशमलव संख्या 7.48657782019270142689973133822016 को भिन्न \frac{11697777844051095979530830215969}{10000000000} में रूपांतरित करें. 1 को निकालकर और रद्द करके भिन्न \frac{11697777844051095979530830215969}{10000000000} को न्यूनतम पदों तक कम करें.

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

64558736119771056212369977545857700093089334767336350659700329 और 1562500000000000000000000000000 का लघुत्तम समापवर्त्य 100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000 है. \frac{3238222219322764578514187360614793750000000000000000000000000000}{64558736119771056212369977545857700093089334767336350659700329} और \frac{11697777844051095979530830215969}{1562500000000000000000000000000} को 100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000 हर वाले भिन्न में रूपांतरित करें.

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

चूँकि \frac{5059722217691819653928417750960615234375000000000000000000000000000000000000000000000000000000}{100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000} और \frac{755193753021799083572852173276890524858698368644990171879009323293911055544430132267890353801}{100873025187142275331828089915402656395452085573963047905781764062500000000000000000000000000} के पास समान भिन्न हैं, उनके अंशों को जोड़कर उन्हें जोड़ें.

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

5814915970713618737501269924237505759233698368644990171879009323293911055544430132267890353801 को प्राप्त करने के लिए 5059722217691819653928417750960615234375000000000000000000000000000000000000000000000000000000 और 755193753021799083572852173276890524858698368644990171879009323293911055544430132267890353801 को जोड़ें.

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