If x=a sin theta and you=b tan theta. Prove that a2/x2-b2/y2=1

 

If x=a sin theta and you=b tan theta. Prove that a2/x2-b2/y2=1

Answer:

Given, 

x=a sinθ

y=b tanθ

To prove:

a2/x2-b2/y2=1

LHS:

a^2/x^2-b^2/y^2

a/(a sinθ)^2-b^2/(b tanθ)^2

1/sinθ-1/(tanθ)^2

=(coscec θ)^2-(cot θ)^2

=1                                              bescause (coscec θ)^2=1+(cot θ)^2