Question

Solve the equation in the given Domain:

1-cos theta/ sin theta = sqr3, 0degrees <or equal to theta < 369 degrees


cos4x + cos 2x =0, 0<or equal to x < pi

Answer 1

Recall that

1-cos theta/ sin theta = tan(theta/2)

so, we want tan(theta/2) = sqrt(3)
theta/2 = 60
theta = 120

Note that theta/2 = 240 also works, but that requires theta=480, outside the domain given.
___________________________

2cos^2(2x) - 1 + cos(2x) = 0
(2cos2x - 1)(cos2x + 1) = 0

cos2x = 1/2, so 2x = 60,300, so x=30,150
cos2x = -1, so 2x = 180, so x=90