tg(2x)*tgx=1

Solution for tg(2x)*tgx=1 equation:

Simplifying
tg(2x) * tgx = 1

Remove parenthesis around (2x)
gt * 2x * tgx = 1

Reorder the terms for easier multiplication:
2gt * x * gtx = 1

Multiply gt * x
2gtx * gtx = 1

Multiply gtx * gtx
2g2t2x2 = 1

Solving
2g2t2x2 = 1

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Divide each side by '2t2x2'.
g2 = 0.5t-2x-2

Simplifying
g2 = 0.5t-2x-2

Take the square root of each side:
g = {-0.707106781t-1x-1, 0.707106781t-1x-1}