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Please solve for x if sin x+cos x-sin 2x+cos 2x-cos 3x=1.

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bushin487 | Student | (Level 1) eNoter

Posted March 21, 2012 at 4:46 AM via web

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Please solve for x if sin x+cos x-sin 2x+cos 2x-cos 3x=1.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted March 22, 2012 at 12:42 AM (Answer #1)

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You need to isolate the terms containing sin x and sin 2x to the right and the terms containing cos x, cos 2x, cos 3x to the left side such that:

`cos x + cos 2x - cos 3x = 1 - sin x + sin 2x`

You need to substitute 0 for x in equation above such that:

`cos0 + cos 2*0 - cos 3*0 = 1 - sin0 + sin 2*0`

You need to substitute 1 for cos 0 and 0 for cos 0 such that:

`1 + 1 - 1 = 1 - 0 + 0`

`1= 1`

Since this substitution checks the equation, then x=0 is considered the solution to the equation `cos x + cos 2x - cos 3x = 1 - sin x + sin 2x.`

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