To solve this equation, we will first expand both sides using the properties of trigonometric functions.

Starting with the left side:
1 - ctg(2a)

We know that cotangent is the reciprocal of tangent, so we can rewrite this as:

1 - 1/tan(2a)

We can take the reciprocal of tan(2a) by using the identity tan(x) = sin(x)/cos(x):

1 - cos(2a)/sin(2a)

Next, we will multiply both the numerator and denominator by sin(2a) to get a common denominator:

sin(2a)/sin(2a) - cos(2a)/sin(2a)

This simplifies to:

sin(2a) - cos(2a)/sin(2a)

Now moving on to the right side:
(1 + ctg(2a))(sin(2a) - cos(2a))

Expanding this using the same steps as above, we get:

(1 + 1/tan(2a))(sin(2a) - cos(2a))
(sin(2a) - cos(2a) + sin(2a) - cos(2a)/sin(2a))

Simplifying this further:

2sin(2a) - 2cos(2a)/sin(2a)

Therefore, the equation simplifies to:

sin(2a) - cos(2a)/sin(2a) = 2sin(2a) - 2cos(2a)/sin(2a)