Simplify: \((1 - \sin \theta)(1 + \sin \theta)\).
FURTHER MATHEMATICS
WAEC 2014
Simplify: \((1 - \sin \theta)(1 + \sin \theta)\).
- A. \(\sin^{2} \theta\)
- B. \(\sec^{2} \theta\)
- C. \(\tan^{2} \theta\)
- D. \(\cos^{2} \theta\)
Correct Answer: D. \(\cos^{2} \theta\)
Explanation
\((1 + \sin \theta)(1 - \sin \theta) = 1 - \sin \theta + \sin \theta - \sin^{2} \theta\)
\(= 1 - \sin^{2} \theta\)
Recall, \(\cos^{2} \theta + \sin^{2} \theta = 1\)
\(\therefore 1 - \sin^{2} \theta = \cos^{2} \theta\).
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