Solve 2tan^-1(1/5)+sec^-1(frac{5sqrt{2}}{7})+2tan^-1(1/8)

$$2 \tan ^ { - 1 } ( \frac { 1 } { 5 } ) + \sec ^ { - 1 } ( \frac { 5 \sqrt { 2 } } { 7 } ) + 2 \tan ^ { - 1 } ( \frac { 1 } { 8 } )$$

Evaluate

$$\frac{283851356967619078404976616143212500000000000}{190416555906588320435298305619341382486413}\approx 1490.686330378$$

Solution Steps

Evaluate trigonometric functions in the problem

$$2 \cdot 0.00349067268159625 ^ {-1} + 1.0001554371821728 ^ {-1} + 2 \cdot 0.00218166502631261 ^ {-1}$$

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

$$2\times \frac{800000000000000}{2792538145277}+1.0001554371821728^{-1}+2\times 0.00218166502631261^{-1}$$

Multiply 2 and \frac{800000000000000}{2792538145277} to get \frac{1600000000000000}{2792538145277}.

$$\frac{1600000000000000}{2792538145277}+1.0001554371821728^{-1}+2\times 0.00218166502631261^{-1}$$

Calculate 1.0001554371821728 to the power of -1 and get \frac{312500000000000}{312548574119429}.

$$\frac{1600000000000000}{2792538145277}+\frac{312500000000000}{312548574119429}+2\times 0.00218166502631261^{-1}$$

Add \frac{1600000000000000}{2792538145277} and \frac{312500000000000}{312548574119429} to get \frac{500950386761485462500000000000}{872803815480441223150286833}.

$$\frac{500950386761485462500000000000}{872803815480441223150286833}+2\times 0.00218166502631261^{-1}$$

Calculate 0.00218166502631261 to the power of -1 and get \frac{100000000000000000}{218166502631261}.

$$\frac{500950386761485462500000000000}{872803815480441223150286833}+2\times \frac{100000000000000000}{218166502631261}$$

Multiply 2 and \frac{100000000000000000}{218166502631261} to get \frac{200000000000000000}{218166502631261}.

$$\frac{500950386761485462500000000000}{872803815480441223150286833}+\frac{200000000000000000}{218166502631261}$$

Add \frac{500950386761485462500000000000}{872803815480441223150286833} and \frac{200000000000000000}{218166502631261} to get \frac{283851356967619078404976616143212500000000000}{190416555906588320435298305619341382486413}.

$$\frac{283851356967619078404976616143212500000000000}{190416555906588320435298305619341382486413}$$