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If Cot x/Cot y = A and Cosec x/Cosec y = B, then the value of Cosec y in terms of A and B.

If Cot x/Cot y = A and Cosec x/Cosec y = B, then the value of Cosec y in terms of A and B. Correct Answer <p>√((1 – A<sup>2</sup>)/(B<sup>2</sup> – A<sup>2</sup>))</p>

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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