frac{sin3^{circ}sin84^{circ}sin87^{circ}}{sin12^{circ}}-frac{sin^{2}27^{circ}-cos^{2}27^{circ}}{2sin6^circcos6^circ(3-4sin^212^circ)} का समाधान करें

$$\frac { \sin 3 ^ { \circ } \sin 84 ^ { \circ } \sin 87 ^ { \circ } } { \sin 12 ^ { \circ } } - \frac { \sin ^ { 2 } 27 ^ { \circ } - \cos ^ { 2 } 27 ^ { \circ } } { 2 \sin 6 ^ { \circ } \cos 6 ^ { \circ } ( 3 - 4 \sin ^ { 2 } 12 ^ { \circ } ) }$$

मूल्यांकन करें

$$\frac{107911000512775026917055443408919316779890884913062057631792086466736686481041}{33833371706466818736292319830373191000111189050000000000000000000000000000000}\approx 3.189484082$$

हल करने वाले चरण

सवाल में त्रिकोणमितीय फ़ंक्शन का मूल्‍यांकन करें

$$\frac{0.05233595624294383 \cdot 0.9945218953682733 \cdot 0.9986295347545738}{0.20791169081775931} - \frac{0.45399049973954675 ^ {2} - 0.8910065241883679 ^ {2}}{2 \cdot 0.10452846326765346 \cdot 0.9564956763167232}$$

0.052049254398643513504402375988739 प्राप्त करने के लिए 0.05233595624294383 और 0.9945218953682733 का गुणा करें.

$$\frac{0.052049254398643513504402375988739\times 0.9986295347545738}{0.20791169081775931}-\frac{0.45399049973954675^{2}-0.8910065241883679^{2}}{2\times 0.10452846326765346\times 0.9564956763167232}$$

0.0519779227044398258017752025124954343964775444382 प्राप्त करने के लिए 0.052049254398643513504402375988739 और 0.9986295347545738 का गुणा करें.

$$\frac{0.0519779227044398258017752025124954343964775444382}{0.20791169081775931}-\frac{0.45399049973954675^{2}-0.8910065241883679^{2}}{2\times 0.10452846326765346\times 0.9564956763167232}$$

अंश और हर दोनों 10000000000000000000000000000000000000000000000000 से गुणा करके \frac{0.0519779227044398258017752025124954343964775444382}{0.20791169081775931} को विस्तृत करें.

$$\frac{519779227044398258017752025124954343964775444382}{2079116908177593100000000000000000000000000000000}-\frac{0.45399049973954675^{2}-0.8910065241883679^{2}}{2\times 0.10452846326765346\times 0.9564956763167232}$$

2 को निकालकर और रद्द करके भिन्न \frac{519779227044398258017752025124954343964775444382}{2079116908177593100000000000000000000000000000000} को न्यूनतम पदों तक कम करें.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{0.45399049973954675^{2}-0.8910065241883679^{2}}{2\times 0.10452846326765346\times 0.9564956763167232}$$

2 की घात की 0.45399049973954675 से गणना करें और 0.2061073738537633976795858954355625 प्राप्त करें.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{0.2061073738537633976795858954355625-0.8910065241883679^{2}}{2\times 0.10452846326765346\times 0.9564956763167232}$$

2 की घात की 0.8910065241883679 से गणना करें और 0.79389262614623663165984166575041 प्राप्त करें.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{0.2061073738537633976795858954355625-0.79389262614623663165984166575041}{2\times 0.10452846326765346\times 0.9564956763167232}$$

-0.5877852522924732339802557703148475 प्राप्त करने के लिए 0.79389262614623663165984166575041 में से 0.2061073738537633976795858954355625 घटाएं.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{-0.5877852522924732339802557703148475}{2\times 0.10452846326765346\times 0.9564956763167232}$$

0.20905692653530692 प्राप्त करने के लिए 2 और 0.10452846326765346 का गुणा करें.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{-0.5877852522924732339802557703148475}{0.20905692653530692\times 0.9564956763167232}$$

0.199962046335083909067305240684544 प्राप्त करने के लिए 0.20905692653530692 और 0.9564956763167232 का गुणा करें.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{-0.5877852522924732339802557703148475}{0.199962046335083909067305240684544}$$

अंश और हर दोनों 10000000000000000000000000000000000 से गुणा करके \frac{-0.5877852522924732339802557703148475}{0.199962046335083909067305240684544} को विस्तृत करें.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{-5877852522924732339802557703148475}{1999620463350839090673052406845440}$$

15 को निकालकर और रद्द करके भिन्न \frac{-5877852522924732339802557703148475}{1999620463350839090673052406845440} को न्यूनतम पदों तक कम करें.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\left(-\frac{391856834861648822653503846876565}{133308030890055939378203493789696}\right)$$

-\frac{391856834861648822653503846876565}{133308030890055939378203493789696} का विपरीत \frac{391856834861648822653503846876565}{133308030890055939378203493789696} है.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}+\frac{391856834861648822653503846876565}{133308030890055939378203493789696}$$

1039558454088796550000000000000000000000000000000 और 133308030890055939378203493789696 का लघुत्तम समापवर्त्य 33833371706466818736292319830373191000111189050000000000000000000000000000000 है. \frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000} और \frac{391856834861648822653503846876565}{133308030890055939378203493789696} को 33833371706466818736292319830373191000111189050000000000000000000000000000000 हर वाले भिन्न में रूपांतरित करें.

$$\frac{8458342926616704407721757006270970284559525574500045913042086466736686481041}{33833371706466818736292319830373191000111189050000000000000000000000000000000}+\frac{99452657586158322509333686402648346495331359338562011718750000000000000000000}{33833371706466818736292319830373191000111189050000000000000000000000000000000}$$

चूँकि \frac{8458342926616704407721757006270970284559525574500045913042086466736686481041}{33833371706466818736292319830373191000111189050000000000000000000000000000000} और \frac{99452657586158322509333686402648346495331359338562011718750000000000000000000}{33833371706466818736292319830373191000111189050000000000000000000000000000000} के पास समान भिन्न हैं, उनके अंशों को जोड़कर उन्हें जोड़ें.

$$\frac{8458342926616704407721757006270970284559525574500045913042086466736686481041+99452657586158322509333686402648346495331359338562011718750000000000000000000}{33833371706466818736292319830373191000111189050000000000000000000000000000000}$$

107911000512775026917055443408919316779890884913062057631792086466736686481041 को प्राप्त करने के लिए 8458342926616704407721757006270970284559525574500045913042086466736686481041 और 99452657586158322509333686402648346495331359338562011718750000000000000000000 को जोड़ें.

$$\frac{107911000512775026917055443408919316779890884913062057631792086466736686481041}{33833371706466818736292319830373191000111189050000000000000000000000000000000}$$