If a cot A + b cosec A=p and b cot A +a cosec A =q then p2-q2 is equal to :
(A) a2-b2 (B) b2-a2 (C) a2+b2 (D) b-a
[A=theta]

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Solution

Hi!

Given, a cot A + b cosec A= p and b cot A + a cosec A = q

p² – q²
= (a cotA + b cosec A)² – (b cotA + a cosecA)²
= (a cot²A + b² cosec² A + 2ab cotA cosecA) – (b² cot²A + a²cosec²A + 2ab cotA cosecA)
= a² cot²A + b² cosec² A + 2ab cotA cosecA – b² cot²A – a²cosec²A – 2ab cotA cosecA
= a² (cot²A – cosec² A) + b² (cosec²A – cot²A)
= b² (cosec²A – cot²A) – a² (cosec²A – cot²A)
= b² – a² (cosec²θ – cot²θ = 1)

Cheers!

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