Solve (1/2)+tan^-1(1/3)+tan^-1(1/8)

$$( \frac { 1 } { 2 } ) + \tan ^ { - 1 } ( \frac { 1 } { 3 } ) + \tan ^ { - 1 } ( \frac { 1 } { 8 } )$$

Evaluate

$$\frac{100073013939771926108936260588049}{158656947845002217872521176098}\approx 630.750908164$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(\frac{1}{2})} + 0.005817829810955344 ^ {-1} + 0.00218166502631261 ^ {-1}$$

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

$$\frac{1}{2}+\frac{62500000000000000}{363614363184709}+0.00218166502631261^{-1}$$

Add \frac{1}{2} and \frac{62500000000000000}{363614363184709} to get \frac{125363614363184709}{727228726369418}.

$$\frac{125363614363184709}{727228726369418}+0.00218166502631261^{-1}$$

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

$$\frac{125363614363184709}{727228726369418}+\frac{100000000000000000}{218166502631261}$$

Add \frac{125363614363184709}{727228726369418} and \frac{100000000000000000}{218166502631261} to get \frac{100073013939771926108936260588049}{158656947845002217872521176098}.

$$\frac{100073013939771926108936260588049}{158656947845002217872521176098}$$

Factor

$$\frac{101 \cdot 463 \cdot 1019 \cdot 1117 \cdot 3307 \cdot 149867 \cdot 3793560801829}{2 \cdot 7 \cdot 13 \cdot 67 \cdot 223 \cdot 251 \cdot 991 \cdot 58174771 \cdot 4032050689} = 630\frac{1.1913679742051257 \times 10^{29}}{1.5865694784500226 \times 10^{29}} = 630.7509081640528$$