Question

If 2cos 2x=1,then find the value of x

Answer 1

SOLUTION

GIVEN

$\displaystyle\sf{2 \cos 2x = 1}$

TO DETERMINE

The value of x

EVALUATION

Here it is given that

$\displaystyle\sf{2 \cos 2x = 1}$

We solve for x as below

$\displaystyle\sf{2 \cos 2x = 1}$

$\displaystyle\sf{ \implies \: \cos 2x = \frac{1}{2} }$

$\displaystyle\sf{ \implies \: \cos 2x = \cos \: \frac{\pi}{3} }$

$\displaystyle\sf{ \implies \: 2x = 2n\pi + \frac{\pi}{3} }$

$\displaystyle\sf{ \implies \: x = n\pi + \frac{\pi}{6} }$

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