Respuesta :
Answer:
The general solution of [tex]cos x = cos(\frac{\pi }{6})[/tex] is
x = 2nπ±[tex]\frac{\pi }{6}[/tex]
The general solution values
[tex]x = - \frac{\pi }{6} and x = \frac{\pi }{6}[/tex]
Step-by-step explanation:
Explanation:-
Given equation is
[tex]2cosx-\sqrt{3} =0 for 0<x<2\pi[/tex]
[tex]2cosx =\sqrt{3}[/tex]
Dividing '2' on both sides, we get
[tex]cos x =\frac{\sqrt{3} }{2}[/tex]
[tex]cos x = cos(\frac{\pi }{6})[/tex]
General solution of cos θ = cos ∝ is θ = 2nπ±∝
Now The general solution of [tex]cos x = cos(\frac{\pi }{6})[/tex] is
x = 2nπ±[tex]\frac{\pi }{6}[/tex]
put n=0
[tex]x = - \frac{\pi }{6} and x = \frac{\pi }{6}[/tex]
Put n=1
[tex]x = 2\pi +\frac{\pi }{6} = \frac{13\pi }{6}[/tex]
[tex]x = 2\pi -\frac{\pi }{6} = \frac{11\pi }{6}[/tex]
put n=2
[tex]x = 4\pi +\frac{\pi }{6} = \frac{25\pi }{6}[/tex]
[tex]x = 4\pi -\frac{\pi }{6} = \frac{23\pi }{6}[/tex]
And so on
But given 0 < x< 2π
The general solution values
[tex]x = - \frac{\pi }{6} and x = \frac{\pi }{6}[/tex]
