If b cosθ = a, then find the value of cosec2θ + cot2θ.

cosθ =\(\frac{a}{b}\)=\(\frac{Base}{Hyp.}\)

Perp. =\(\sqrt {b^2-a^2}\)

⇒ cosec²θ + cot²θ = \(\frac{hyp^2}{Perp^2}\) + \(\frac{base^2}{Per^2}\) = \(\frac{b^2}{(\sqrt {b^2-a^2})^2}\) + \(\frac{a^2}{(\sqrt {b^2-a^2})^2}\)

= \(\frac{b^2}{b^2-a^2}\) + \(\frac{a^2}{b^2-a^2}\)

= \(\frac{b^2\;+\;a^2}{b^2-a^2}\)