Question

Attaching the question below, please help :)

Answer 1

2 * cos² x - 1 = 0

<=>

2 * cos² x = 1

<=>

cos² x = 1/2

<=>

cos x = - sqr (1/2) or cos x = sqr (1/2)

<=>

cos x = - sqr (2) / 2 or cos x = sqr (2) / 2

<=>

x = 3pi/4 or x = 5pi/4 or x = 7pi/4 or x = pi/4


Answers :

pi/4 ; 3pi/4 ; 5pi/4 ; 7pi/4 ===> radians

45 ; 135 ; 225 ; 315 ===> degrees

Answer 2

but would -7pi/4 be an answer? or 15pi/4, i don't understand how to put that in the answer choices @Nurali

Answer 3

A and B

Answer 4

thank you!

Answer 5

I would have approached this using the Cosine Double-Angle Formula:\[\Large\rm 2\cos^2x-1=0\qquad\to\qquad \cos2x=0\]Ummm these are always a lil tricky...
So we have...\[\Large\rm 2x=\frac{\pi}{2}+k \pi\]This angle is zero at pi/2 and every multiple of pi added or subtracted as well.
Solve for x by dividing by 2,\[\Large\rm x=\frac{\pi}{4}+\frac{k \pi}{2}\]When k=1,\[\Large\rm x=\frac{\pi}{4}+\frac{\pi}{2}=\frac{3\pi}{4}\qquad \color{green}{\checkmark}\]So option A looks good.

Letting k=7,
\[\Large\rm x=\frac{\pi}{4}+\frac{7\pi}{2}=\frac{15\pi}{4}\qquad\color{green}{\checkmark}\]Option B also looks good!


It turns out option D is also correct though! :d
Let's not forget that one! :)
k=-4,
\[\Large\rm x=\frac{\pi}{4}+\frac{-4\pi}{2}=\frac{-7\pi}{4}\qquad\color{green}{\checkmark}\]