Question

If a cot θ + b cosec θ = p and b cot θ + a cosec θ = q, then p²− q² =
A. a²− b²
B. b²− a²
C. a²+ b²
D. b − a

Answer 1

Answer:

option B is the right answer

Answer 2

B. b²− a²

Step-by-step explanation:

Given: p = a.cotθ + b.cosecθ --------------(1)

q = a.cosecθ + b.cotθ --------------(2)

So p² – q² = (a.cotθ + b.cosecθ)² - (a.cosecθ + b.cotθ)²

= a²cot²θ +b²cosec²θ +2ab.cotθ.cosecθ - a²cosec²θ - b²cot²θ - 2ab.cotθ.cosecθ

= a²cot²θ +b²cosec²θ - a²cosec²θ - b²cot²θ

= b² (cosec²θ - cot²θ) -a² (cosec²θ - cot²θ)

= b² (1) -a² (1)

p²–q² = b²-a²

Option B is the answer.