Ok, let's verify this given identity.
We know that the relation sin²x + cos²x = 1 is an important trigonometric identity. We will use it to verify the identity sin²β + sin²(π/2-β) = 1.
1. We have the expression sin²β + sin²(π/2 - β).
2. We can use the complementary angle identity sin(π/2 - x) = cos(x) to rewrite sin²(π/2 - β) as cos²β.
3. This simplifies our equation to sin²β + cos²β.
4. Now, applying the Pythagorean identity, sin²x + cos²x = 1, we see that sin²β + cos²β equals 1.
5. Therefore, we have verified the identity sin²β + sin²(π/2 - β) = 1.
So, by simplifying at each step using known trigonometric identities, we have been able to confirm that this identity is indeed correct, proving the relation as true.