Question

If (cos $\theta$ + sec $\theta$) = $\frac{5}{2}$ then $(co{s}^2\theta +se{c}^2\theta )$ = ?

(a) $\frac{21}{4}$ (b) $\frac{17}{4}$ (c) $\frac{29}{4}$ (d) $\frac{33}{4}$

Answer 1

(cos $\theta$ + sec $\theta$) = $\frac{5}{2}$

squaring both sides

$co{s}^2\theta +se{c}^2\theta +2cos\theta sec\theta =25/4$

$co{s}^2\theta +se{c}^2\theta +2\times 1=\frac{25}{4}$

$(co{s}^2\theta +se{c}^2\theta )=\frac{25}{4}-2$

$=\frac{25-8}{4}=\frac{17}{4}$