Question

General value of x satisfying the equation tan^2x+sec2x=1 is

Answer 1

multiplying by cos2x,
sin2x +1 =cos2x ie 2sinxcosx + 1= 1- 2sin^2x
so, 2sinxcosx + 2sin^2x = 0 2sinx(cosx + sinx) = 0 sinx =0 or sinx +cos x =0 ie sinx/cosx + 1 =0
i.e. sinx =0 or tanx = -1
i.e. x = π∙n for n ∈ any integer or x = π∙k - π/4 for k ∈ any integer