Simplify: \((1 – \sin \theta)(1 + \sin \theta)\).
- \(\sin^{2} \theta\)
- \(\sec^{2} \theta\)
- \(\tan^{2} \theta\)
-
\(\cos^{2} \theta\)
The correct answer is: D
Explanation
\((1 + \sin \theta)(1 - \sin \theta) = 1 - \sin \theta + \sin \theta - \sin^{2} \theta\)
\(= 1 - \sin^{2} \theta\)
Recall, \(\cos^{2} \theta + \sin^{2} \theta = 1\)
\(\therefore 1 - \sin^{2} \theta = \cos^{2} \theta\).