If (cos θ + sec θ ) = $\dfrac{5}{2}$, find the value of (cos²θ + sec²θ).

Given,

(cos θ + sec θ ) = $\dfrac{5}{2}$

Squaring both sides,

cos²θ + sec²θ + 2cos θ sec θ = $\dfrac{25}{4}$

As we know cos θ = $\dfrac{1}{\sec θ }$

cos²θ + sec²θ + 2 = $\dfrac{25}{4}$

$\Rightarrow \cos^2θ + \sec^2θ = \dfrac{25}{4} - 2$

$\Rightarrow \dfrac{25 - 8}{4} = \dfrac{17}{4}$

Hence, cos²θ + sec²θ = $\dfrac{17}{4}$.