Question

Find the general solution for the following equation:

$se{c}^2$ 2x = 1 - tan 2x

Answer 1

${\text{sec}}^2$ 2x = 1 - tan 2x

$\Rightarrow 1+{\text{tan}}^2$ 2x = 1 - tan 2x

$\Rightarrow {\text{tan}}^2$ 2x+ tan 2x = 0

$\Rightarrow$ tan 2x (tan 2x+1)= 0

Either tan 2x =0 or tan 2x + 1 = 0

$\Rightarrow$ 2x = $n\pi$ or tan 2x =-1

=- tan $\frac{\pi }{4}$ = tan $(-\frac{\pi }{4})$, n $ϵ$ Z

$\Rightarrow x=\frac{n\pi }{2}$ or $x=\frac{n\pi }{2}+\frac{3\pi }{8}$, n $ϵ$ Z.