Verify the identity:

(1+tan^2u) (1-sin^2u) = 1

=> The first expression on the left: (1 + tan²)

we know that tangent = sin/cos

so tan² = sin²/cos²

the expression is (1 + sin²/cos²)

=> The second expression on the left: (1 - sin²)

we know that (sin² + cos²) = 1

subtract sin² from each side,

and we have (1 - sin²) = (cos²)

=> Multiply the massaged form of the two expressions:

(1 + tan²) (1 - sin²) = (1 + sin²/cos²) (cos²) = (cos² + sin²) = 1 qed