Question

1. $2\tan^{2}\theta = 2$

Explanation:

Step1: Isolate $\tan^{2}\theta$

Divide both sides of the equation $2\tan^{2}\theta = 2$ by 2. We get $\tan^{2}\theta=\frac{2}{2}=1$.

Step2: Solve for $\tan\theta$

Take the square - root of both sides. So $\tan\theta=\pm\sqrt{1}=\pm1$.

Step3: Find the values of $\theta$

When $\tan\theta = 1$, $\theta = n\pi+\frac{\pi}{4},n\in\mathbb{Z}$; when $\tan\theta=-1$, $\theta = n\pi - \frac{\pi}{4},n\in\mathbb{Z}$. In degrees, when $\tan\theta = 1$, $\theta = 180^{\circ}n + 45^{\circ},n\in\mathbb{Z}$; when $\tan\theta=-1$, $\theta=180^{\circ}n - 45^{\circ},n\in\mathbb{Z}$.

Answer:

$\theta = n\pi\pm\frac{\pi}{4},n\in\mathbb{Z}$ (in radians) or $\theta = 180^{\circ}n\pm45^{\circ},n\in\mathbb{Z}$ (in degrees)