Answer:
The solution of the given trigonometric equation
[tex]x = \frac{\pi }{6}[/tex]
Step-by-step explanation:
Step(i):-
Given
[tex]cos( 3x - \frac{\pi }{3} ) = \frac{\sqrt{3} }{2}[/tex]
[tex]cos( 3x - \frac{\pi }{3} ) = cos (\frac{\pi }{6} )[/tex]
[tex]3x - \frac{\pi }{3} = \frac{\pi }{6}[/tex]
[tex]3x - \frac{\pi }{3 } + \frac{\pi }{3} = \frac{\pi }{6} + \frac{\pi }{3}[/tex]
[tex]3x = \frac{2\pi +\pi }{6} = \frac{3\pi }{6} = \frac{\pi }{2}[/tex]
[tex]x = \frac{\pi }{6}[/tex]
Step(ii):-
The solution of the given trigonometric equation
[tex]x = \frac{\pi }{6}[/tex]
verification :-
[tex]cos( 3x - \frac{\pi }{3} ) = \frac{\sqrt{3} }{2}[/tex]
put [tex]x = \frac{\pi }{6}[/tex]
[tex]cos( 3(\frac{\pi }{6}) - \frac{\pi }{3} ) = \frac{\sqrt{3} }{2}[/tex]
[tex]cos (\frac{\pi }{6} ) = \frac{\sqrt{3} }{2} \\\\\frac{\sqrt{3} }{2} = \frac{\sqrt{3} }{2}[/tex]
Both are equal
∴The solution of the given trigonometric equation
[tex]x = \frac{\pi }{6}[/tex]