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Solve sin x-3 sin 2x + sin 3x = cos x -3...

Solve `sin x-3 sin 2x + sin 3x = cos x -3 cos 2x + cos 3x`.

Text Solution

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The given equation is
`sin x-3 sin 2x + sin 3x=cos x-3 cos 2x+cos 3x`
`rArr 2 sin 2x cos x-3 sin 2x=2 cos 2x cos x-3 cos 2x`
`rArr sin 2x(2 cos x-3)=cos 2x(2 cos x-3)`
`rArr sin 2x=cos 2x" "("As "cos x ne 3//2)`
`rArr tan 2x=1`
`rArr 2x=n pi+pi//4`
`rArr x=(npi)/2+pi/8, n in Z`
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