a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2

1.	a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to …(1) a2 – b2(2) b2 – a2(3) a2 + b2(4) b – a
Answer» (2) b² – a² p² – q² = (p + q) (p – q) = (a cot θ + b cosec θ + b cot θ + a cosec θ) (a cot θ + b cosec θ – b cot θ – a cosec θ) = [cot θ (a + b) + cosec θ (a + b)] [cot θ (a – b) + cosec θ (b – a)] = (a + b) [cot θ + cosec θ] (a – b) [cosec θ (a – b)] = (a + b) [cot θ + cosec θ] (a – b) [cot θ – cosec θ] = (a + b) (a – b) (cot² θ – cosec² θ) = (a² – b²) (-1) = – (a² – b²) p² – q² = b² – a²

a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to …(1) a2 – b2(2) b2 – a2(3) a2 + b2(4) b – a

Answer»

(2) b² – a²

p² – q² = (p + q) (p – q)

= (a cot θ + b cosec θ + b cot θ + a cosec θ) (a cot θ + b cosec θ – b cot θ – a cosec θ)

= [cot θ (a + b) + cosec θ (a + b)] [cot θ (a – b) + cosec θ (b – a)]

= (a + b) [cot θ + cosec θ] (a – b) [cosec θ (a – b)]

= (a + b) [cot θ + cosec θ] (a – b) [cot θ – cosec θ]

= (a + b) (a – b) (cot² θ – cosec² θ)

= (a² – b²) (-1) = – (a² – b²)

p² – q² = b² – a²