다음을 풀어보세요: left(tan(1*8)right)^2-left(tan(1*2)right)^2/1-left(tan(1*8)right)^2left(tan(1*2)right)^2

$$\frac{ { \left( \tan ( 1 \cdot 8 ) \right) }^{ 2 } - { \left( \tan ( 1 \cdot 2 ) \right) }^{ 2 } }{ 1- { \left( \tan ( 1 \cdot 8 ) \right) }^{ 2 } { \left( \tan ( 1 \cdot 2 ) \right) }^{ 2 } }$$

계산

$$\frac{1723931728088291891652816657948800000000000000000000000000000000}{93021015214617905190606995322390538903324483365707164114672738477}\approx 0.018532712$$

해답 단계

Evaluate trigonometric functions in the problem

$$\frac{0.14054083470239145 ^ {2} - 0.03492076949174773 ^ {2}}{1 - 0.14054083470239145 ^ {2} 0.03492076949174773 ^ {2}}$$

0.14054083470239145의 2제곱을 계산하여 0.0197517262188449168482923490331025을(를) 구합니다.

$$\frac{0.0197517262188449168482923490331025-0.03492076949174773^{2}}{1-0.14054083470239145^{2}\times 0.03492076949174773^{2}}$$

0.03492076949174773의 2제곱을 계산하여 0.0012194601418957790130245699601529을(를) 구합니다.

$$\frac{0.0197517262188449168482923490331025-0.0012194601418957790130245699601529}{1-0.14054083470239145^{2}\times 0.03492076949174773^{2}}$$

0.0197517262188449168482923490331025에서 0.0012194601418957790130245699601529을(를) 빼고 0.0185322660769491378352677790729496을(를) 구합니다.

$$\frac{0.0185322660769491378352677790729496}{1-0.14054083470239145^{2}\times 0.03492076949174773^{2}}$$

0.14054083470239145의 2제곱을 계산하여 0.0197517262188449168482923490331025을(를) 구합니다.

$$\frac{0.0185322660769491378352677790729496}{1-0.0197517262188449168482923490331025\times 0.03492076949174773^{2}}$$

0.03492076949174773의 2제곱을 계산하여 0.0012194601418957790130245699601529을(를) 구합니다.

$$\frac{0.0185322660769491378352677790729496}{1-0.0197517262188449168482923490331025\times 0.0012194601418957790130245699601529}$$

0.0197517262188449168482923490331025과(와) 0.0012194601418957790130245699601529을(를) 곱하여 0.00002408644285751920097480028430170678926180381864798576726806137225(을)를 구합니다.

$$\frac{0.0185322660769491378352677790729496}{1-0.00002408644285751920097480028430170678926180381864798576726806137225}$$

1에서 0.00002408644285751920097480028430170678926180381864798576726806137225을(를) 빼고 0.99997591355714248079902519971569829321073819618135201423273193862775을(를) 구합니다.

$$\frac{0.0185322660769491378352677790729496}{0.99997591355714248079902519971569829321073819618135201423273193862775}$$

분자와 분모 모두에 100000000000000000000000000000000000000000000000000000000000000000000을(를) 곱하여 \frac{0.0185322660769491378352677790729496}{0.99997591355714248079902519971569829321073819618135201423273193862775}을(를) 확장합니다.

$$\frac{1853226607694913783526777907294960000000000000000000000000000000000}{99997591355714248079902519971569829321073819618135201423273193862775}$$

1075을(를) 추출 및 상쇄하여 분수 \frac{1853226607694913783526777907294960000000000000000000000000000000000}{99997591355714248079902519971569829321073819618135201423273193862775}을(를) 기약 분수로 약분합니다.

$$\frac{1723931728088291891652816657948800000000000000000000000000000000}{93021015214617905190606995322390538903324483365707164114672738477}$$