Answer:
[tex]sin^2(\theta)[/tex]
Step-by-step explanation:
Step 1: Take out cos from both sides of the minus
[tex]sec(\theta)\ cos(\theta)-cos^2(\theta)[/tex]
[tex]cos(\theta)*(sec(\theta)-cos(\theta))[/tex]
Step 2: Convert sec to 1/cos and distribute
[tex]cos(\theta)*(\frac{1}{cos(\theta)}-cos(\theta))[/tex]
[tex](\frac{1*cos(\theta)}{cos(\theta)})-(cos(\theta)*cos(\theta)})[/tex]
[tex]1-cos^2(\theta)[/tex]
Step 3: Simplify
[tex]1-cos^2(\theta)[/tex] can also be interpreted as [tex]sin^2(\theta)[/tex]
Answer: [tex]sin^2(\theta)[/tex]
