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Solve cos theta+cos 2theta+cos 3theta=0....

Solve `cos theta+cos 2theta+cos 3theta=0`.

Text Solution

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The correct Answer is:
`theta=(2n+1) pi/4 or theta = 2npi pm (2pi)/3, n in Z`
`cos theta + cos 2 theta + cos 3 theta = 0`
or `(cos theta + cos 3 theta) + cos 2 theta = 0`
or `2 cos theta cos 2 theta + cos 2 theta = 0`
or `cos 2 theta (2 cos theta + 1) = 0`
or `cos 2 theta = 0 or 2 cos theta + 1 = 0`
`rArr 2 theta = (2n + 1) pi//2 or cos theta = - 1/2, n in Z`
or `theta = (2n + 1) pi//4 or theta = 2n pi -+ 2pi//3, AA n in Z`
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