Answer: sin²θ
Explanation:
First, convert sec into [tex]\frac{1}{cos}[/tex], then use identity (cos²θ + sin²θ = 1) and simplify:
[tex]\frac{sec^{2}\theta - 1}{sec^{2}\theta}[/tex]
= [tex]\frac{sec^{2}\theta - 1}{1}*\frac{1}{sec^{2}\theta}[/tex]
= [tex](\frac{1}{cos^{2}\theta} - 1)*(\frac{sec^{2}\theta}{1})[/tex]
= [tex](\frac{1}{cos^{2}\theta} - \frac{cos^{2}\theta}{cos^{2}\theta})*(\frac{cos^{2}\theta}{1})[/tex]
= [tex](\frac{1 - cos^{2}\theta}{cos^{2}\theta})*(\frac{cos^{2}\theta}{1})[/tex]
= [tex](\frac{sin^{2}\theta}{cos^{2}\theta})*(\frac{cos^{2}\theta}{1})[/tex]
= [tex]\frac{sin^{2}\theta*cos^{2}\theta}{cos^{2}\theta}[/tex]
= sin²θ
