Your thinking (and your notation) is a little fuzzy . . .
It says that the sum of their derivatives is zero.
These two seem to imply that . . . . . no
We have this right triangle:Code:* * β| a * | * | x * | * α | * - - - - - - - - *
We see that and are in the same right triangle.
. . They are complementary: .
Now differntiate . . .
. . and you'll see why the sum of the derivatives is zero.