Solve for t in (0,2pi) sin 2t - 3 = 6 sin t - cost

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We have to solve sin 2t - 3 = 6 sin t - cos t for x.

Now sin 2t = 2 sin t cos t

sin 2t - 3 = 6 sin  t- cos t

=> 2sin t *cos t -3  = 6 sin t - cos t

=> 2sin t *cos t - 6 sin t + cos t - 3  = 0

=> 2 sin t( cost - 3) +1 ( cos t - 3) = 0

=> ( 2 sin t  +2) ( cos t -3) = 0

For 2 sin t + 2 = 0

=> sin t = -2/2 = -1

=> t = arc sin (-1)= -90 degree

For cos t -3 =0, we don't have any value of t as cos t > 1.

Therefore t = -90 degrees.

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