# Answer to Question #8750 in Calculus for maci

Question #8750

cos 2t + 6 sin^2 t = 2

Expert's answer

cos 2t=1-2sin^2 t

So

1-2sin^2 t+6 sin^2 t = 2

4 sin^2 t = 1

sin^2 t = 1/4

whence sin t = 1/2 or sin t = -1/2

Therefore& t=pie/6+2pie k, t=5pie/6+2 pie k, t=-pie/6+2 pie k, t=-5pie/6+2pie k where k-integer (pie=3,1415926...)

So

1-2sin^2 t+6 sin^2 t = 2

4 sin^2 t = 1

sin^2 t = 1/4

whence sin t = 1/2 or sin t = -1/2

Therefore& t=pie/6+2pie k, t=5pie/6+2 pie k, t=-pie/6+2 pie k, t=-5pie/6+2pie k where k-integer (pie=3,1415926...)

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