If cot θ = 7/8, then the value of (1 + sin θ)(1 - sin θ) / (1 + cos θ)(1 - cos θ) is:
Correct: A
The given expression is (1 + sin θ)(1 - sin θ) / (1 + cos θ)(1 - cos θ).
Using the algebraic identity (a + b)(a - b) = a² - b²:
Numerator: (1 + sin θ)(1 - sin θ) = 1² - sin² θ = cos² θ.
Denominator: (1 + cos θ)(1 - cos θ) = 1² - cos² θ = sin² θ.
So, the expression simplifies to cos² θ / sin² θ.
We know that cos θ / sin θ = cot θ.
Therefore, cos² θ / sin² θ = (cot θ)².
Given cot θ = 7/8.
So, (cot θ)² = (7/8)² = 49/64.