(Tgx-1)(tgx+1)=0
This can be simplified to tg^2(x) - 1 = 0
Tangent is a periodic function with period π so solutions for x will be:

x = π/4 + kπ, 3π/4 + kπ, k belonging to Z

2sin^2x-3sinx-2=0
Let y = sinx
Now the equation becomes:
2y^2 - 3y - 2 = 0
Solving this quadratic equation by factorization, we get:

y = 2 or y = -1/2

Since sinx can only be between -1 and 1, sinx can only be -1/2.
Therefore, sinx = -1/2 implies:

x = 7π/6 + 2kπ, 11π/6 + 2kπ, k belonging to Z

2cos^2x+cosx-6=0
This is a quadratic equation in terms of cosx:
2cos^2(x) + cosx - 6 = 0

Solving the quadratic equation, we get:

cosx = 1/2 or cosx = -3

The solutions for cosx = 1/2 are:

x = π/3 + 2kπ or x = 5π/3 + 2kπ

The solution for cosx = -3 has no real solutions, as cosine function varies between -1 and 1.