If x = a c o s e c θ and y = b c o t θ , then which of the following equations is true ? Options: A . &nbspx2−y2=a2−b2 B . &nbspx2a2−y2b2=1 C . &nbspx2+y2=a2+b2 D . &nbspx2a2+y2b2=1

If x=a cosec θ and y=b cot θ, then which of the

Question

x = a c o s e c θ

and

y = b c o t θ

, then which of the following equations is true ?

Options:

A . x2−y2=a2−b2

B . x2a2−y2b2=1

C . x2+y2=a2+b2

D . x2a2+y2b2=1

Answer: Option B
:
B

x = a c o s e c θ \Rightarrow \frac{x}{a} = c o s e c θ

.....(1)

y = b c o t θ \Rightarrow \frac{y}{b} = c o t θ

.....(2)
Squaring the equations and subtracting (2) from (1) we get,

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = c o s e c^{2} θ - c o t^{2} θ

∴ \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1.... (1 + c o t^{2} θ = c o s e c^{2} θ)

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