حل 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)}

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

ارزیابی

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

مراحل راه‌حل

Evaluate trigonometric functions in the problem

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

2 را بر 2 برای به دست آوردن 1 تقسیم کنید.

$$\frac{1\times 0.05233595624294383\times 0.9945218953682733\times 0.9986295347545738}{0.20791169081775931}-\frac{0.45399049973954675^{2}-0.8910065241883679^{2}}{2\times 0.10452846326765346\times 0.9564956763167232}$$

1 و 0.05233595624294383 را برای دستیابی به 0.05233595624294383 ضرب کنید.

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

0.05233595624294383 و 0.9945218953682733 را برای دستیابی به 0.052049254398643513504402375988739 ضرب کنید.

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

0.052049254398643513504402375988739 و 0.9986295347545738 را برای دستیابی به 0.0519779227044398258017752025124954343964775444382 ضرب کنید.

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

\frac{0.0519779227044398258017752025124954343964775444382}{0.20791169081775931} را با ضرب در صورت و مخرج 10000000000000000000000000000000000000000000000000 بسط دهید.

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

کسر \frac{519779227044398258017752025124954343964775444382}{2079116908177593100000000000000000000000000000000} را با ریشه گرفتن و ساده کردن 2، به کمترین عبارت‌ها کاهش دهید.

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

0.45399049973954675 را به توان 2 محاسبه کنید و 0.2061073738537633976795858954355625 را به دست آورید.

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

0.8910065241883679 را به توان 2 محاسبه کنید و 0.79389262614623663165984166575041 را به دست آورید.

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

تفریق 0.79389262614623663165984166575041 را از 0.2061073738537633976795858954355625 برای به دست آوردن -0.5877852522924732339802557703148475 تفریق کنید.

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

2 و 0.10452846326765346 را برای دستیابی به 0.20905692653530692 ضرب کنید.

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

0.20905692653530692 و 0.9564956763167232 را برای دستیابی به 0.199962046335083909067305240684544 ضرب کنید.

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

\frac{-0.5877852522924732339802557703148475}{0.199962046335083909067305240684544} را با ضرب در صورت و مخرج 10000000000000000000000000000000000 بسط دهید.

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

کسر \frac{-5877852522924732339802557703148475}{1999620463350839090673052406845440} را با ریشه گرفتن و ساده کردن 15، به کمترین عبارت‌ها کاهش دهید.

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

متضاد -\frac{391856834861648822653503846876565}{133308030890055939378203493789696} عبارت است از \frac{391856834861648822653503846876565}{133308030890055939378203493789696}.

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

کوچک‌ترین مضرب مشترک 1039558454088796550000000000000000000000000000000 و 133308030890055939378203493789696 عبارت است از 33833371706466818736292319830373191000111189050000000000000000000000000000000. \frac{259889613522199129008876012562477171982387722191}{1039558454088796550000000000000000000000000000000} و \frac{391856834861648822653503846876565}{133308030890055939378203493789696} را به کسرهایی مخرج 33833371706466818736292319830373191000111189050000000000000000000000000000000 تبدیل کنید.

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

از آنجا که \frac{8458342926616704407721757006270970284559525574500045913042086466736686481041}{33833371706466818736292319830373191000111189050000000000000000000000000000000} و \frac{99452657586158322509333686402648346495331359338562011718750000000000000000000}{33833371706466818736292319830373191000111189050000000000000000000000000000000} دارای مخرج مشترک هستند، با افزودن صورت کسرها آنها را جمع کنید.

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

8458342926616704407721757006270970284559525574500045913042086466736686481041 و 99452657586158322509333686402648346495331359338562011718750000000000000000000 را برای دریافت 107911000512775026917055443408919316779890884913062057631792086466736686481041 اضافه کنید.

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