You have (or someone else has) submitted this question at least once before, and you have received responses indicating that there is no solution.
The reason for that is you have not shown the equation correctly. What you have shown is
That equation says the cosine of some angle plus 20 is equal to the sine of some other angle. Since the ranges of both sine and cosine are between -1 and 1, there is obviously not going to be a solution.
Almost certainly the equation you intended to show is
That equation says the cosine of some angle is equal to the sine of some other angle. There will be solutions to that equation.
For a starting point, note that in a right triangle the sine of one acute angle is the cosine of the other acute angle, and vice versa. So one solution will be when the sum of the angle measures a+20 and a is equal to 90 degrees.
The "primary" solution to the equation is a = 35 degrees; that gives us cos(55) = sin(35) -- which is true because those angles sum to 90 degrees.
After that, since sine and cosine are both periodic, there will be solutions at 180 degree increments from the primary solution. So the complete solution set is
a = 35 + 180k
where k is an integer (positive, negative, or zero).
