Simplify: \((1 - \sin \theta)(1 + \sin \theta)\).
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Correct Answer: Option D
Explanation:
\((1 + \sin \theta)(1 - \sin \theta) = 1 - \sin \theta + \sin \theta - \sin^{2} \theta\)
\(= 1 - \sin^{2} \theta\)
Recall, \(\cos^{2} \theta + \sin^{2} \theta = 1\)
\(\therefore 1 - \sin^{2} \theta = \cos^{2} \theta\).
\((1 + \sin \theta)(1 - \sin \theta) = 1 - \sin \theta + \sin \theta - \sin^{2} \theta\)
\(= 1 - \sin^{2} \theta\)
Recall, \(\cos^{2} \theta + \sin^{2} \theta = 1\)
\(\therefore 1 - \sin^{2} \theta = \cos^{2} \theta\).