If $$tan^{2} θ = 1 - e^{2}$$ , then the value of $$secθ + tan^{3} θ cosecθ$$ is

we know , 1 + $$tan^2 \theta$$ = $$sec^2 \theta$$

given that $$tan^{2} θ = 1 - e^{2}$$

$$sec^2 \ theta$$ - 1 = 1- $$e^2$$

$$sec^2 \theta$$ = 2- $$e^2$$...........(1)

Now , $$secθ + tan^{3} θ cosecθ$$ = $$sec \theta + tan^{2} \theta tan \theta cosec \theta$$

= $$sec \theta(1+ tan^2 \theta)$$ = $$sec^3 \theta$$................(2)

Using equation 1 and 2

$$secθ + tan^{3} θ cosecθ$$ = $$(2-e^2)^\frac{3}{2}$$