Do you want to solve sin(x-20) + cos(x-20) = 0? If so:

sin(x-20°) + cos(x-20°) = 0

cos(x-20°) = cos(20°-x)

sin(x-20°) = -sin(20°-x)

-sin(20°-x) + cos(20°-x) = 0

cos(20°-x) = sin(20°-x)

divide both sides by cos(20°-x)

1 = tan(20°-x)

tan(20°-x) = 1

20°-x = 45°

x-20° = -45°

x = 20-45 = -25°

x = 335° <------- solution 1

20°-x = 180°+45°

20°-x = 225°

x-20° = -225°

x= -205°

x = 155° <------ solution 2

If Sin (x-20°) + cos (x-20°) = 0

Then tan(x - 20) = - 1

x - 20 = -45

x = - 25

x = 155, 335

you have not listed any equation, just a statement.

The integral of sin is -cos.

The integral of cos is sin.

So the integral of this function is -cos(x - 20) + sin(x - 20). Plug in 360 degrees. Plug in 0 degrees. Those are equivalent angles, so when you subtract the result is 0.