Solve {left(tan(pi/18)right)}^2+{left(tan(5pi/18)right)}^2+{left(tan(7pi/18)right)}^2

$${ \left( \tan ( \frac{ \pi }{ 18 } ) \right) }^{ 2 } + { \left( \tan ( \frac{ 5 \pi }{ 18 } ) \right) }^{ 2 } + { \left( \tan ( \frac{ 7 \pi }{ 18 } ) \right) }^{ 2 }$$

Evaluate

$$8.9999999999999963709639505511729604$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.17632698070846498 ^ {2} + 1.19175359259421 ^ {2} + 2.7474774194546216 ^ {2}$$

Calculate 0.17632698070846498 to the power of 2 and get 0.0310912041257633812202434278864004.

$$0.0310912041257633812202434278864004+1.19175359259421^{2}+2.7474774194546216^{2}$$

Calculate 1.19175359259421 to the power of 2 and get 1.4202766254612062681577255241.

$$0.0310912041257633812202434278864004+1.4202766254612062681577255241+2.7474774194546216^{2}$$

Add 0.0310912041257633812202434278864004 and 1.4202766254612062681577255241 to get 1.4513678295869696493779689519864004.

$$1.4513678295869696493779689519864004+2.7474774194546216^{2}$$

Calculate 2.7474774194546216 to the power of 2 and get 7.54863217041302672158598159918656.

$$1.4513678295869696493779689519864004+7.54863217041302672158598159918656$$

Add 1.4513678295869696493779689519864004 and 7.54863217041302672158598159918656 to get 8.9999999999999963709639505511729604.

$$8.9999999999999963709639505511729604$$

Factor

$$\frac{3 \cdot 7499999999999996975803292125977467}{2 ^ {32} \cdot 5 ^ {34}} = 8\frac{2.499999999999992 \times 10^{33}}{2.5 \times 10^{33}} = 8.999999999999996$$