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What are all the exact solutions of square root 2 cosx-1=0 for 0 less than or equal to x less than or equal to 2 pi ?Give your answer in radians.

What are all the exact solutions of square root 2 cosx10 for 0 less than or equal to x less than or equal to 2 pi Give your answer in radians class=

Respuesta :

Answer: [tex]x=\frac{\pi}{4}\ or\ \frac{7\pi}{4}[/tex]

Step-by-step explanation:

Given equation is

[tex]\sqrt{2}\cos x-1=0[/tex]

solving this

[tex]\sqrt{2}\cos x=1\\\cos x=\frac{1}{\sqrt{2}}[/tex]

There can be two solution because [tex]0<x<2\pi[/tex]

[tex]\cos x=\cos \frac{\pi }{4}\ or\ \cos (2\pi -\frac{\pi}{4})\\[/tex]

so, [tex]x=\frac{\pi}{4}\ or\ \frac{7\pi}{4}[/tex]