1.

If Cot x/Cot y = A and Cosec x/Cosec y = B, then the value of Cosec y in terms of A and B.1.√((1 – A2)/(B2 – A2))2. (1 – A2)/(A2 – B2)3. A/(B2 – A2)4. (1 – B2)/(B2 – A2)

Answer» Correct Answer - Option 1 :

√((1 – A2)/(B2 – A2))


Given

Cot x/Cot y = A and Cosec x/Cosec y = B

Concept

Cosec2 A – Cot2A = 1

Calculation

Cot x = A Cot y

Squaring on both sides

Cot2x = A2Cot2y

⇒  Cosec 2x – 1 = A 2 (Cosec 2 y – 1)     ---- (1)

Cosec x = B Cosec y

Squaring on both sides

⇒  Cosec 2x = B 2Cosec 2 y    ---- (2)

From (1) and (2)

B2Cosec2y – 1 = A2Cosec2y – A2

⇒  B2Cosec2y – A2Cosec2y = - A2 + 1

⇒  Cosec2y(B2– A2) = - A2+ 1

⇒  Cosec y = √((1 – A2)/(B2 – A2))


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