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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]

                     

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