Question

BRAINLIESTTT ASAP! PLEASE HELP ME :)

Answer 1

Answer:

$\large \boxed{x = 0 \text{ and } x = \pi}$

Step-by-step explanation:

$\begin{array}{rcl}\tan^{2}x\sec^{2}x + 2\sec^{2}x - \tan^{2}x & = & 2\\\tan^{2}x\sec^{2}x - \tan^{2}x + 2\sec^{2}x - 2 & = & 0\\\tan^{2}x(\sec^{2}x -1) + 2(\sec^{2}x - 1) & = & 0\\(\tan^{2}x + 2)(\sec^{2}x - 1)& = & 0\\\tan^{2}x + 2 = 0 & \qquad & \sec^{2}x - 1 = 0\\\end{array}$

$\begin{array}{rcl}\tan^{2}x = -2 & \qquad & \sec^{2}x = 1\\\tan x = \sqrt{-2} & \qquad & \sec x = \sqrt{1}\\\textbf{No solution} & \qquad & \sec x = \pm 1\\& \qquad &\dfrac{1}{\cos x} \qquad \pm 1 \\\\\cos x = 1 &\qquad & \cos x = -1&\\x = \mathbf{0}&\qquad&x = \pi\\\end{array}\\\text{The solutions are \large \boxed{\mathbf{x = 0} \textbf{ and } \mathbf{x = \pi}} }$

The graph of your function is shown below with solutions at (0, 0) and (π,0).