Question

$\frac{4}{8} = \frac{1}{2tan^2}$

$\forall \epsilon > 0.$

Answer 1

$\tan^2 = 1$

Answer 2

The given equation is: $\frac{4}{8} = \frac{1}{2\tan^2}$

Step 1: Simplify the left side of the equation. The fraction $\frac{4}{8}$ can be simplified to $\frac{1}{2}$. $\frac{1}{2} = \frac{1}{2\tan^2}$

Step 2: Solve for $\tan^2$. To isolate $\tan^2$, we can take the reciprocal of both sides of the equation. $2 = 2\tan^2$ Now, divide both sides by 2: $\frac{2}{2} = \tan^2$ $1 = \tan^2$ So, the value of $\tan^2$ is 1.

The condition $\forall \epsilon > 0$ is typically used in calculus for definitions of limits or continuity and is irrelevant to solving this algebraic trigonometric equation.