Question

What are all the exact solutions of square root2 cosx -1 = 0 for 0 <= x <= 2pi? Give you answer in radians.

Answer 1

Answer:

Option 2 - $x=\frac{\pi}{4},\frac{7\pi}{4}$  

Step-by-step explanation:

Given : Expression $\sqrt{2}\cos x-1=0$ for $0\leq x\leq 2\pi$              

To find : What are all the exact solutions of expression?

Solution :  

First we simplify the expression,

$\sqrt{2}\cos x-1=0$

$\sqrt{2}\cos x=1$            

$\cos x=\frac{1}{\sqrt{2}}$      

The general solution is            

$x=\frac{\pi}{4}+2\pi n,\frac{7\pi}{4}+2\pi n$          

For $0\leq x\leq 2\pi$                  

The solution is  $x=\frac{\pi}{4},\frac{7\pi}{4}$  

Therefore, Option 2 is correct.

Answer 2

Answer:

pi/4 and 7pi/4

Step-by-step explanation:

attached

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