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

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

Baholash

$$\frac{107911000512775026917055443408919316779890884913062057631792086466736686481041}{33833371706466818736292319830373191000111189050000000000000000000000000000000}\approx 3,189484082$$

Yechim qadamlari

Evaluate trigonometric functions in the problem

$$\frac{\frac{2}{2} 0,05233595624294383 \cdot 0,9945218953682733 \cdot 0,9986295347545738}{0,20791169081775931} - \frac{0,45399049973954675 ^ {2} - 0,8910065241883679 ^ {2}}{2 \cdot 0,10452846326765346 \cdot 0,9564956763167232}$$

1 ni olish uchun 2 ni 2 ga bo‘ling.

$$\frac{1\times 0,05233595624294383\times 0,9945218953682733\times 0,9986295347545738}{0,20791169081775931}-\frac{0,45399049973954675^{2}-0,8910065241883679^{2}}{2\times 0,10452846326765346\times 0,9564956763167232}$$

0,05233595624294383 hosil qilish uchun 1 va 0,05233595624294383 ni ko'paytirish.

$$\frac{0,05233595624294383\times 0,9945218953682733\times 0,9986295347545738}{0,20791169081775931}-\frac{0,45399049973954675^{2}-0,8910065241883679^{2}}{2\times 0,10452846326765346\times 0,9564956763167232}$$

0,052049254398643513504402375988739 hosil qilish uchun 0,05233595624294383 va 0,9945218953682733 ni ko'paytirish.

$$\frac{0,052049254398643513504402375988739\times 0,9986295347545738}{0,20791169081775931}-\frac{0,45399049973954675^{2}-0,8910065241883679^{2}}{2\times 0,10452846326765346\times 0,9564956763167232}$$

0,0519779227044398258017752025124954343964775444382 hosil qilish uchun 0,052049254398643513504402375988739 va 0,9986295347545738 ni ko'paytirish.

$$\frac{0,0519779227044398258017752025124954343964775444382}{0,20791169081775931}-\frac{0,45399049973954675^{2}-0,8910065241883679^{2}}{2\times 0,10452846326765346\times 0,9564956763167232}$$

\frac{0,0519779227044398258017752025124954343964775444382}{0,20791169081775931} kasrini uning surat va maxrajini 10000000000000000000000000000000000000000000000000 ga ko‘paytirish bilan kengaytiring.

$$\frac{519779227044398258017752025124954343964775444382}{2079116908177593100000000000000000000000000000000}-\frac{0,45399049973954675^{2}-0,8910065241883679^{2}}{2\times 0,10452846326765346\times 0,9564956763167232}$$

\frac{519779227044398258017752025124954343964775444382}{2079116908177593100000000000000000000000000000000} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{0,45399049973954675^{2}-0,8910065241883679^{2}}{2\times 0,10452846326765346\times 0,9564956763167232}$$

2 daraja ko‘rsatkichini 0,45399049973954675 ga hisoblang va 0,2061073738537633976795858954355625 ni qiymatni oling.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{0,2061073738537633976795858954355625-0,8910065241883679^{2}}{2\times 0,10452846326765346\times 0,9564956763167232}$$

2 daraja ko‘rsatkichini 0,8910065241883679 ga hisoblang va 0,79389262614623663165984166575041 ni qiymatni oling.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{0,2061073738537633976795858954355625-0,79389262614623663165984166575041}{2\times 0,10452846326765346\times 0,9564956763167232}$$

-0,5877852522924732339802557703148475 olish uchun 0,2061073738537633976795858954355625 dan 0,79389262614623663165984166575041 ni ayirish.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{-0,5877852522924732339802557703148475}{2\times 0,10452846326765346\times 0,9564956763167232}$$

0,20905692653530692 hosil qilish uchun 2 va 0,10452846326765346 ni ko'paytirish.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{-0,5877852522924732339802557703148475}{0,20905692653530692\times 0,9564956763167232}$$

0,199962046335083909067305240684544 hosil qilish uchun 0,20905692653530692 va 0,9564956763167232 ni ko'paytirish.

$$\frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000}-\frac{-0,5877852522924732339802557703148475}{0,199962046335083909067305240684544}$$

\frac{-0,5877852522924732339802557703148475}{0,199962046335083909067305240684544} kasrini uning surat va maxrajini 10000000000000000000000000000000000 ga ko‘paytirish bilan kengaytiring.

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

\frac{-5877852522924732339802557703148475}{1999620463350839090673052406845440} ulushini 15 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

-\frac{391856834861648822653503846876565}{133308030890055939378203493789696} ning teskarisi \frac{391856834861648822653503846876565}{133308030890055939378203493789696} ga teng.

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

1039558454088796550000000000000000000000000000000 va 133308030890055939378203493789696 ning eng kichik umumiy karralisi 33833371706466818736292319830373191000111189050000000000000000000000000000000 ga teng. \frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000} va \frac{391856834861648822653503846876565}{133308030890055939378203493789696} ni 33833371706466818736292319830373191000111189050000000000000000000000000000000 maxraj bilan kasrlarga aylantirib oling.

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

\frac{8458342926616704407721757006270970284559525574500045913042086466736686481041}{33833371706466818736292319830373191000111189050000000000000000000000000000000} va \frac{99452657586158322509333686402648346495331359338562011718750000000000000000000}{33833371706466818736292319830373191000111189050000000000000000000000000000000} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

107911000512775026917055443408919316779890884913062057631792086466736686481041 olish uchun 8458342926616704407721757006270970284559525574500045913042086466736686481041 va 99452657586158322509333686402648346495331359338562011718750000000000000000000'ni qo'shing.

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