(1)

special angles , it is positive so x = 30 , 210

(2)

11.54 is the basic angle , X should be in the first and second quadrant as it is positive .

(3)

sin x -1 = 2 cos x - 2 sinx cos x

sin x-1 = 2 cos x ( 1 - sinx )

1 - sinx = - 2 cosX(1-sin x)

1 = -2cos X

cos X = - 1/2

X = 120 and 240

(3)