Question

√x+1=a sin theta , √y+1=b cosec theta​

Answer 1

Answer:

$\mathrm {ab = \sqrt{(x+1)(y+1)} }$

Step-by-step explanation:

Given :

√(x+1)=a sinθ , √(y+1)=b cosecθ

To find :

Eliminate θ from the equations

Solution :

First, let us find what are sinθ and cosecθ

sinθ = √(x+1)/a ; cosecθ = √(y+1)/b ___ [1]

We know that,

$\boxed{\mathrm{sin\theta \times cosec\theta = 1}}$

So, multiplying by 1, we get,

$\implies \mathrm {1 = \dfrac{\sqrt{(x+1)(y+1)} }{ab} }$

$\implies \underline {\boxed{\mathbf {ab = \sqrt{(x+1)(y+1)}}}}$

Hope it helps!!