Question

1. Eliminate θ from the given equations, x = a cot θ – b cosec θ y = a cot θ + b cosec θ Solution: x = a cot θ – b cosec θ …(I) y = a cot θ + b cosec θ …(II) Adding equations (I) and (II), x + y = ∴ cot θ = + Subtracting equation (I) from (II), y – x = ∴ cosec θ = Now, cosec2 θ – cot2 θ = 1 …(Identity) ∴ ( − ) − = 1 ∴ (−) − (+) = 1 ∴ ( − ) − ( ∗ ) =

Answer 1

Answer:

ANSWER

We have,

x=a(cscθ+cotθ)                  ……. (1)

y=b(cscθ−cotθ)                  …….. (2)

 From equation (1) and (2), we get

xy=ab(cscθ+cotθ)(cscθ−cotθ)

xy=ab(csc2θ−cot2θ)

xy=ab[∵csc2x−cot2x=1]

 Hence, this is the answer.