Solve tan^-11/5+tan^-11/7+tan^-111/23=pi/4

$$\tan ^ { - 1 } \frac { 1 } { 5 } + \tan ^ { - 1 } \frac { 1 } { 7 } + \tan ^ { - 1 } \frac { 11 } { 23 } = \frac { \pi } { 4 }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$0.00349067268159625 ^ {-1} + 0.0024933326696033225 ^ {-1} + 0.008347420730439625 ^ {-1} = \frac{\pi}{4}$$

Multiply both sides of the equation by 4.

$$4\times 0.00349067268159625^{-1}+4\times 0.0024933326696033225^{-1}+4\times 0.008347420730439625^{-1}=\pi$$

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

$$4\times \frac{800000000000000}{2792538145277}+4\times 0.0024933326696033225^{-1}+4\times 0.008347420730439625^{-1}=\pi$$

Multiply 4 and \frac{800000000000000}{2792538145277} to get \frac{3200000000000000}{2792538145277}.

$$\frac{3200000000000000}{2792538145277}+4\times 0.0024933326696033225^{-1}+4\times 0.008347420730439625^{-1}=\pi$$

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

$$\frac{3200000000000000}{2792538145277}+4\times \frac{400000000000000000}{997333067841329}+4\times 0.008347420730439625^{-1}=\pi$$

Multiply 4 and \frac{400000000000000000}{997333067841329} to get \frac{1600000000000000000}{997333067841329}.

$$\frac{3200000000000000}{2792538145277}+\frac{1600000000000000000}{997333067841329}+4\times 0.008347420730439625^{-1}=\pi$$

Add \frac{3200000000000000}{2792538145277} and \frac{1600000000000000000}{997333067841329} to get \frac{7659526849535452800000000000000}{2785090635493045299786753133}.

$$\frac{7659526849535452800000000000000}{2785090635493045299786753133}+4\times 0.008347420730439625^{-1}=\pi$$

Calculate 0.008347420730439625 to the power of -1 and get \frac{8000000000000000}{66779365843517}.

$$\frac{7659526849535452800000000000000}{2785090635493045299786753133}+4\times \frac{8000000000000000}{66779365843517}=\pi$$

Multiply 4 and \frac{8000000000000000}{66779365843517} to get \frac{32000000000000000}{66779365843517}.

$$\frac{7659526849535452800000000000000}{2785090635493045299786753133}+\frac{32000000000000000}{66779365843517}=\pi$$

Add \frac{7659526849535452800000000000000}{2785090635493045299786753133} and \frac{32000000000000000}{66779365843517} to get \frac{600621246009146642104244639753600000000000000}{185986586454943324615181101773723187488761}.

$$\frac{600621246009146642104244639753600000000000000}{185986586454943324615181101773723187488761}=\pi$$

Compare \frac{600621246009146642104244639753600000000000000}{185986586454943324615181101773723187488761} and \pi .

$$\text{false}$$