Question

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Answer 1

Answer:

The solution of the given trigonometric equation

                   $x = \frac{\pi }{6}$

Step-by-step explanation:

Step(i):-

Given  

                $cos( 3x - \frac{\pi }{3} ) = \frac{\sqrt{3} }{2}$

                  $cos( 3x - \frac{\pi }{3} ) = cos (\frac{\pi }{6} )$

                      $3x - \frac{\pi }{3} = \frac{\pi }{6}$

                      $3x - \frac{\pi }{3 } + \frac{\pi }{3} = \frac{\pi }{6} + \frac{\pi }{3}$

                      $3x = \frac{2\pi +\pi }{6} = \frac{3\pi }{6} = \frac{\pi }{2}$

                     $x = \frac{\pi }{6}$

Step(ii):-

The solution of the given trigonometric equation

                   $x = \frac{\pi }{6}$

verification :-

      $cos( 3x - \frac{\pi }{3} ) = \frac{\sqrt{3} }{2}$

put  $x = \frac{\pi }{6}$

    $cos( 3(\frac{\pi }{6}) - \frac{\pi }{3} ) = \frac{\sqrt{3} }{2}$

    $cos (\frac{\pi }{6} ) = \frac{\sqrt{3} }{2} \\\\\frac{\sqrt{3} }{2} = \frac{\sqrt{3} }{2}$

Both are equal

∴The solution of the given trigonometric equation

                   $x = \frac{\pi }{6}$