Solve left(tan(1*8)right)^2-left(tan(1*2)right)^2/1-left(tan(1*8)right)^2left(tan(1*2)right)^2

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

Evaluate

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

Solution Steps

Evaluate trigonometric functions in the problem

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

Calculate 0.14054083470239145 to the power of 2 and get 0.0197517262188449168482923490331025.

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

Calculate 0.03492076949174773 to the power of 2 and get 0.0012194601418957790130245699601529.

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

Subtract 0.0012194601418957790130245699601529 from 0.0197517262188449168482923490331025 to get 0.0185322660769491378352677790729496.

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

Calculate 0.14054083470239145 to the power of 2 and get 0.0197517262188449168482923490331025.

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

Calculate 0.03492076949174773 to the power of 2 and get 0.0012194601418957790130245699601529.

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

Multiply 0.0197517262188449168482923490331025 and 0.0012194601418957790130245699601529 to get 0.00002408644285751920097480028430170678926180381864798576726806137225.

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

Subtract 0.00002408644285751920097480028430170678926180381864798576726806137225 from 1 to get 0.99997591355714248079902519971569829321073819618135201423273193862775.

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

Expand \frac{0.0185322660769491378352677790729496}{0.99997591355714248079902519971569829321073819618135201423273193862775} by multiplying both numerator and the denominator by 100000000000000000000000000000000000000000000000000000000000000000000.

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

Reduce the fraction \frac{1853226607694913783526777907294960000000000000000000000000000000000}{99997591355714248079902519971569829321073819618135201423273193862775} to lowest terms by extracting and canceling out 1075.

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