Find the general solution of the equation cos4x=cos2x

Asked by Pragya Singh | 1 year ago |  65

##### Solution :-

Here it is given that, cos4x=cos2x

Which implies,

cos4x-cos2x=0

Now we know that,

cosA-cosB=-2sin$$( \dfrac{A+B}{2})sin( \dfrac{A-B}{2})$$

Therefore we have,

$$-2sin= ( \dfrac{4x+2x}{2})sin( \dfrac{4x-2x}{2})=0$$

sin3xsinx=0

Hence we have, sin3x=0

Or, sinx=0

Therefore, 3x=nπ

or x=nπ ,where $$n\in Z$$

$$x= \dfrac{n\pi}{3}$$

or x=nπ ,where $$n\in Z$$

Answered by Abhisek | 1 year ago

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