Solve 12sin2t 2sin9t 2 0 for all solution 0 lessthanorequl

Solve 12sin^2(t) + 2sin9t) -2 = 0 for all solution 0 lessthanorequlto to

Solution

12 sin²t +2 sin(t) -2 = 0

12 sin²t + 6 sin t - 4 sin t-2 = 0

6 sin t [ 2 sin t+1] - 2 [ 2 sin t +1]=0

[ 2 sin t +1] [ 6 sin t -2] = 0

ie either [ 2 sin t +1 ] = 0 or [ 6 sin t - 2 ] = 0

when 2sin t + 1 = 0

sin t = -1/2

sin t = - sin (pi/6)

sin t = sin ( pi + pi/6) or sin t = sin ( 2 pi - pi/6)

sin t = sin 7 pi/6 sin t = sin ( 11 pi/6)

t = 7 pi/6 = 210⁰   t = 11 pi/6 = 330⁰

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when 6 sin t - 2 = 0

sin t = 1/3

sin t = sin (19.47) sin t = sin (19.47)

t = 19.47 ⁰   or sin t = sin ( 180 - 19.47)

sin t = sin 160.53

t = 160.53⁰