Solve tan^-11/3-tan^-11/5+tan^-11/7

$$\tan ^ { - 1 } \frac { 1 } { 3 } - \tan ^ { - 1 } \frac { 1 } { 5 } + \tan ^ { - 1 } \frac { 1 } { 7 }$$

Evaluate

$$\frac{290115253786935609538394997403700000000000000}{1012698957836500163803389180572360663443297}\approx 286.477290751$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.005817829810955344 ^ {-1} - 0.00349067268159625 ^ {-1} + 0.0024933326696033225 ^ {-1}$$

Calculate 0.005817829810955344 to the power of -1 and get \frac{62500000000000000}{363614363184709}.

$$\frac{62500000000000000}{363614363184709}-0.00349067268159625^{-1}+0.0024933326696033225^{-1}$$

Calculate 0.00349067268159625 to the power of -1 and get \frac{800000000000000}{2792538145277}.

$$\frac{62500000000000000}{363614363184709}-\frac{800000000000000}{2792538145277}+0.0024933326696033225^{-1}$$

Subtract \frac{800000000000000}{2792538145277} from \frac{62500000000000000}{363614363184709} to get -\frac{116357856467954700000000000000}{1015406979363904741826969393}.

$$-\frac{116357856467954700000000000000}{1015406979363904741826969393}+0.0024933326696033225^{-1}$$

Calculate 0.0024933326696033225 to the power of -1 and get \frac{400000000000000000}{997333067841329}.

$$-\frac{116357856467954700000000000000}{1015406979363904741826969393}+\frac{400000000000000000}{997333067841329}$$

Add -\frac{116357856467954700000000000000}{1015406979363904741826969393} and \frac{400000000000000000}{997333067841329} to get \frac{290115253786935609538394997403700000000000000}{1012698957836500163803389180572360663443297}.

$$\frac{290115253786935609538394997403700000000000000}{1012698957836500163803389180572360663443297}$$

Factor

$$\frac{43 \cdot 12899 \cdot 5230534434559297178948341 \cdot 2 ^ {14} \cdot 5 ^ {14}}{7 \cdot 13 \cdot 61 \cdot 89 \cdot 907 \cdot 991 \cdot 2153 \cdot 13931 \cdot 36923 \cdot 510727099 \cdot 4032050689} = 286\frac{4.8335184569653205 \times 10^{41}}{1.0126989578365002 \times 10^{42}} = 286.4772907505792$$