Question

solve, (sec^(2)θ - cos^(2)θ)^(2) = tanθ - sin^(2)θ , between the range 0<θ<360"

Answer 1

$$\left(\frac {1}{\cos^ {2} \theta} - \cos^ {2} \theta\right) ^ {2} = \tan \theta - \sin^ {2} \theta$$

We can solve it graphically:

And we have next solutions:

$$\left\{ \begin{array}{l} \theta = \pi k, k \in Z \\ \theta = 2 (\pi m - 1.31182), m \in Z \\ \theta = 2 (\pi n + 0.258974), n \in Z \Rightarrow \theta = \{0, 0.517948, \pi, 3.65954, 2\pi \}. \\ \theta \in [0, 2\pi] \end{array} \right.$$

Answer: $\theta = \{0, 0.517948, \pi, 3.65954, 2\pi\}$ .