Question

If (cos θ + sec θ) = $\frac{5}{2}$, then (cos² θ + sec² θ) = ?
(a) $\frac{21}{4}$
(b) $\frac{17}{4}$
(c) $\frac{29}{4}$
(d) $\frac{33}{4}$

Answer 1

(b) $\frac{17}{4}$
We have (cos θ +sec θ) = $\frac{5}{2}$
Squaring both sides, we get:
(cos θ + sec θ)² = ($\frac{5}{2}$)²
$\Rightarrow$cos² θ + sec² θ + 2 cos θ sec θ = $\frac{25}{4}$
$\Rightarrow$cos² θ + sec² θ + 2 = $\frac{25}{4}$ [∵ sec θ = $\frac{1}{\cos \theta }$]
$\Rightarrow$cos² θ + sec² θ = $\frac{25}{4}$ − 2 = $\frac{17}{4}$