To solve the equation tgx - 2ctg(x) = -1 in the interval [0,π/2], we need to first rewrite the equation in terms of sine and cosine using the trigonometric identity:

ctg(x) = 1/tan(x) = cos(x)/sin(x)

Now, the equation becomes:

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

Multiplying both sides by sin(x) to clear the denominator, we get:

sin(x)tan(x) - 2cos(x) = -sin(x)

Now, we can use the trigonometric identity tan(x) = sin(x)/cos(x) to replace tan(x) in the equation:

sin(x)^2/cos(x) - 2cos(x) = -sin(x)

Multiplying through by cos(x) to clear the fraction gives:

sin(x)^2 - 2cos(x)^2 = -sin(x)cos(x)

Now, we can use the Pythagorean identity sin(x)^2 + cos(x)^2 = 1 to write the equation solely in terms of sin(x):

1 - 2(1-sin(x)^2) = -sin(x)(√(1-sin(x)^2))

1 - 2 + 2sin(x)^2 = - sin(x)√(1-sin(x)^2)

2sin(x)^2 - 1 = - sin(x)√(1-sin(x)^2)

2sin(x)^2 + sin(x)√(1-sin(x)^2) - 1 = 0

This is a non-linear equation and needs to be solved using numerical methods such as graphing or numerical approximation. The solution will be the values of x in the interval [0,π/2] that satisfy the equation.