Simplify \frac{\sin^{2}\theta+\cos^{2}\theta}{\cos^{2}\theta}

Simplify $\frac{{\mathrm{sin}}^{2}\theta +{\mathrm{cos}}^{2}\theta }{{\mathrm{cos}}^{2}\theta }$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Cheryl King
${\mathrm{sin}}^{2}\theta +{\mathrm{cos}}^{2}\theta =1$
$1+{\mathrm{tan}}^{2}\theta ={\mathrm{sec}}^{2}\theta$
$\mathrm{sec}\theta =\frac{1}{\mathrm{cos}\theta }$
$⇒\left(\frac{1}{{\mathrm{cos}}^{2}\theta }\right)={\mathrm{sec}}^{2}\theta =\left(1+{\mathrm{tan}}^{2}\theta \right)$

accimaroyalde
Using trig identities:
$\frac{{\mathrm{sin}}^{2}\theta +{\mathrm{cos}}^{2}\theta }{{\mathrm{cos}}^{2}\theta }={\mathrm{sec}}^{2}\theta$