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Solve sqrt(3) cos theta-3 sin theta =4 s...

Solve `sqrt(3) cos theta-3 sin theta =4 sin 2 theta cos 3 theta`.

Text Solution

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We have `sqrt(3) cos theta -3 sin theta=2 (sin 5 theta- sin theta)`
or `(sqrt(3)/2) cos theta-(1/2) sin theta= sin 5 theta`
`rArr cos (theta+pi/6)= sin 5 theta = cos (pi/2- 5 theta)`
`rArr theta + pi/6 = 2n pi pm (pi/2 - 5theta)`
or `theta=(n pi)/3+pi/18 or theta=- (n pi)/2 +pi/6, AA n in Z`
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