1) To solve the equation 2sinx + cos^2x = 1, we can rewrite cos^2x as 1 - sin^2x using the Pythagorean identity for sine and cosine:

2sinx + 1 - sin^2x = 1
2sinx - sin^2x = 0

Now, we can factor out sinx:

sinx(2 - sinx) = 0

This equation is satisfied when sinx = 0 or 2 - sinx = 0.

When sinx = 0, x can be any multiple of π.

When 2 - sinx = 0, sinx = 2, which is not possible. Therefore, the only solution to the equation is x = nπ, where n is an integer.

2) To solve the expression tg(π/4) + sin(π/2), we first calculate the values of tangent and sine at the given angles:

tg(π/4) = 1
sin(π/2) = 1

Now, we can substitute these values into the expression:

1 + 1 = 2

Therefore, the result of tg(π/4) + sin(π/2) is 2.