Question

sec²θ=4+2tan²θ
Find θ​

Answer 1

Recall the Pythagorean identity,

$\sec^2\theta=1+\tan^2\theta$

So we have

$\sec^2\theta=4+2\tan^2\theta$

$1+\tan^2\theta=4+2\tan^2\theta$

$-3=\tan^2\theta$

But squaring any real number always gives a non-negative number, so there are no real solutions to this equation.