Q. 17

# If a cot θ + b cosec θ = p and b cot θ + a cosec θ = q, then p2− q2 =A. a2− b2B. b2− a2C. a2 + b2D. b − a

Given: a cot θ + b cosec θ = p

Squaring both sides, we get

(a cot θ + b cosec θ)2 = p2

a2 cot2 θ + b2 cosec2 θ + 2ab cot θ cosec θ = p2 ……(i)

and b cot θ + a cosec θ = q

Squaring both sides, we get

(b cot θ + a cosec θ)2 = q2

b2 cot2 θ + a2 cosec2 θ + 2ab cot θ cosec θ = q2 ……(ii)

To find: p2 – q2

Subtracting (ii) from (i), we get

a2 cot2 θ + b2 cosec2 θ + 2ab cot θ cosec θ – b2 cot2 θ – a2 cosec2 θ – 2ab cot θ cosec θ = p2 – q2

P2 – q2 = a2 (cot2 θ – cosec2 θ) + b2 (cosec2 θ – cot2 θ)

= a2 ( – 1) + b2 (1) [1 = cosec2 θ – cot2 θ]

= b2 – a2

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Basic Concepts of Trigonometry45 mins  Trigonometric Identities33 mins  Champ Quiz | Trigonometric Identities33 mins  NCERT | Trigonometric Identities52 mins  Trigonometric Identities44 mins  Solving NCERT Questions on Trigonometric Identities56 mins  Algebraic Identities48 mins  Quiz | Practice Important Questions on Trigonometrical Identities46 mins  Quiz | Task on Trigonometric Ratios46 mins  Trick to learn all Trigonometric Formulae28 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 