1) Solve the equation 2cos^2x - cosx - 1 = 0:

Let y = cosx

Substitute y into the equation:

2y^2 - y - 1 = 0

Factor the equation:

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

Solve for y:

y = -1/2 or y = 1

Now substitute back y = cosx:

cosx = -1/2 or cosx = 1

Solve for x:

x = 2π/3 + 2πn, 4π/3 + 2πn or x = 0 + 2πn

2) Solve the equation 4cos^2x - 7sin2x = 2:

Using trigonometric identities:

sin2x = 2sinxcosx

Substitute the identity into the equation:

4cos^2x - 7(2sinxcosx) = 2
4cos^2x - 14sinxcosx = 2
4cos^2x - 14(1/2)sin2x = 2
4cos^2x - 7sin2x = 2

We have already solved this one in Step 1. The solution to the second equation is the same as the first one:

x = 2π/3 + 2πn, 4π/3 + 2πn or x = 0 + 2πn.