Question

cos 2t + 6 sin^2 t = 2

Answer 1

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...)