Question

tan^2 theta-49=0....two solutions possible?

Answer 1

Assuming you're solving for theta:
\[\tan ^2(\theta-49)=\frac{ \sin (\theta-49) }{ \cos(\theta-49) }\]
This = 0 when \[\sin(\theta-49)=0\]
\[\sin(x)=0\] when \[x=0,\pi,2\pi,etc\]
so \[\theta=0, \pi+49, 2\pi+49, etc\]

Answer 2

(tan x -7)(tan x +7)= 0