Eliminate 0 from the following: x = 5 + 6 cosec θ,y = 3 + 8 cot θ

1.	Eliminate 0 from the following: x = 5 + 6 cosec θ,y = 3 + 8 cot θ
Answer» x = 5 + 6cosec θ and y = 3 + 8cot θ ∴ x – 5 = 6cosec θ and y – 3 = 8cot θ ∴ cosec θ = \(\frac{x-5}{6}\) and cot θ \(\frac{y-3}{8}\) We know that, cosec² θ – cot² θ = 1 ∴ \((\frac{x-5}{6})^2 - (\frac{y-3}{8})^2=1\)

Answer»

x = 5 + 6cosec θ and y = 3 + 8cot θ

∴ x – 5 = 6cosec θ and y – 3 = 8cot θ

∴ cosec θ = \(\frac{x-5}{6}\) and cot θ \(\frac{y-3}{8}\)

We know that,

cosec² θ – cot² θ = 1

∴ \((\frac{x-5}{6})^2 - (\frac{y-3}{8})^2=1\)

Discussion