Solve tan22.5^circ/1-tan^222.5^circ=

$$\frac { \tan 22.5 ^ { \circ } } { 1 - \tan ^ { 2 } 22.5 ^ { \circ } } =$$

Evaluate

$$\frac{4142135623730950300000000000000000}{8284271247461901131792063785892991}\approx 0.5$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.41421356237309503}{1 - 0.41421356237309503 ^ {2}}$$

Calculate 0.41421356237309503 to the power of 2 and get 0.1715728752538098868207936214107009.

$$\frac{0.41421356237309503}{1-0.1715728752538098868207936214107009}$$

Subtract 0.1715728752538098868207936214107009 from 1 to get 0.8284271247461901131792063785892991.

$$\frac{0.41421356237309503}{0.8284271247461901131792063785892991}$$

Expand \frac{0.41421356237309503}{0.8284271247461901131792063785892991} by multiplying both numerator and the denominator by 10000000000000000000000000000000000.

$$\frac{4142135623730950300000000000000000}{8284271247461901131792063785892991}$$

Factor

$$\frac{7 \cdot 17 \cdot 47 \cdot 2221 \cdot 19730779 \cdot 2 ^ {17} \cdot 5 ^ {17} \cdot 13 ^ {2}}{3 \cdot 29 \cdot 53 \cdot 9127 \cdot 675071 \cdot 136298689 \cdot 2139390225437} = 0.49999999999999994$$