Question

At what x-values do the graphs of the functions y=cos 2x and y = cos^2 x-1 intersect over the interval 0 ≤ x ≤ pi. There must be two selections there are two anwsers!

Answer 1

Answer:

x=pi/2 and x=3pi/2

Step-by-step explanation:

Answer 2

Answer:

$x=\frac{\pi}{2}$  and  $x=\frac{3\pi}{2}$

Step-by-step explanation:

We need to solve the 2 equations to figure out the x-values (intersecting points).

Note: The identity  $cos^{2}x=\frac{1}{2}+\frac{1}{2}cos(2x)$

$cos(2x)=cos^{2}(x)-1\\cos(2x)=(\frac{1}{2}+\frac{1}{2}cos(2x))-1\\cos(2x)=\frac{1}{2}cos(2x)-\frac{1}{2}\\\frac{1}{2}cos(2x)=-\frac{1}{2}\\cos(2x)=-1\\2x=cos^{-1}(-1)\\2x=\pi, 3\pi\\x=\frac{\pi}{2}, \frac{3\pi}{2}$

So they intersect at  $x=\frac{\pi}{2}, \frac{3\pi}{2}$