Solve for x and show fundamental/general solution: Sin3x = SinXShow complete solution and explain the answer.



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You need to solve for x the trigonometric equation, hence I suggest you to move all terms containing x to the left side such that:

`sin 3x - sin x = 0`

You either may transform the difference of trigonometric functions in a product or you may express sin 3x in terms of sin x.

Selecting the first method yields:

`2cos ((3x+x)/2)*sin ((3x-x)/2) = 0`

You need to divide by 2 bto sides such that:

`cos 2x* sin x = 0 ` => `cos 2x = 0`  or `sin x = 0`  (it is impossible for cos 2x and sin x to be zero simultaneously)

`cos 2x = 0 =gt 2x = +- cos^(-1) 0 + 2n*pi`

`2x = +-(pi/2) + 2n*pi =gt x = +-(pi/4) + n*pi`

`sin x = 0 =gt x = n*pi`

Hence, evaluating the solutions to equation yields `x = n*pi`  and `x = +-(pi/4) + n*pi.`

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