Question

(tan theta -1) (sec theta -1) =0

Answer 1

either \[\tan \theta-1=0\]
\[\tan \theta=1,\theta=n \pi+\frac{ \pi }{ 4 }\]
where n is an integer.

Answer 2

or \[\sec \theta-1=0,\sec \theta=1,\frac{ 1 }{ \cos \theta }=1,\cos \theta=1,\theta=2 n \pi\]
where n is an integer.