I've tried these problems many times but none of my answers seem correct...can someone help?

Question

2cos^2ɵ + cosɵ - 1= 0

and

(cotɵ)(cscɵ - 1/2) = 0

Answer 1

Make a substitution. Let x = cos2t(theta) and you'll have

2x^2 + x-1 = 0

Then factor:

(2x -1)(x +1)=0

x = 1/2 or x = -1

so cost = 1/2 or cost = -1

t = 60 degrees, 120 degrees

or

t = 180 degrees.

In the second one, let cotx = 0 and cscx = 1/2 and now solve for the values that make those equations true.