Question

If cos theta +sec theta =-5/2 then what is the value cos^2 theta +sec^2 theta

Answer 1

If $cos \alpha + sec\alpha =\frac{-5}{2}$ , what is the value of $cos^{2} \alpha +sec^{2} \alpha$ ?

Given,

$cos \alpha + sec\alpha =\frac{-5}{2}$

To find,

$cos^{2} \alpha +sec^{2} \alpha$

Solution,

Given $cos \alpha + sec\alpha =\frac{-5}{2}$

On squaring both sides, we get

$(cos \alpha + sec\alpha) ^{2} = \frac{25}{4}$

⇒ $cos^{2} \alpha + 2cos\alpha sec\alpha +sec^{2} \alpha = \frac{25}{4}$

⇒$cos^{2} \alpha +sec^{2} \alpha = \frac{25}{4}-2cos\alpha sec$

= $\frac{25}{4} -(2cos\alpha *\frac{1}{cos\alpha } )$

= (25/4) - 2

= (25-8)/2

=17/4

∴ $cos^{2} \alpha +sec^{2} \alpha$ = 17/4

#SPJ3