Given: \(a \cos θ = 3\) and \(b \tan θ = 4\), Find the relation between \(a\) and \(b\) that eliminates \(θ\).

Q.Given: \(a \cos θ = 3\) and \(b \tan θ = 4\), Find the relation between \(a\) and \(b\) that eliminates \(θ\).

Given: \(a \cos \theta = 3\) ∴ \(\cos \theta = \cfrac{3}{a}\) ⇒ \(\sec \theta = \cfrac{a}{3}\) Also, \(b \tan \theta = 4\) ⇒ \(\tan \theta = \cfrac{4}{b}\) We know: \(\sec^2 \theta - \tan^2 \theta = 1\) Substituting the values: \(\left(\cfrac{a}{3}\right)^2 - \left(\cfrac{4}{b}\right)^2 = 1\) ⇒ \(\cfrac{a^2}{9} - \cfrac{16}{b^2} = 1\)