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GUJCET · Maths · Determinants
\(\left|\begin{array}{cc}\cos ^2 \theta & -\sin ^2 \theta \\ \sin ^2 \theta & \cos ^2 \theta\end{array}\right|=\) ___________ .
- A \(\frac{1}{2}-\frac{1}{2} \cos ^2 2 \theta\)
- B \(\frac{1}{4}(3+\cos 4 \theta)\)
- C \(1+\frac{1}{2} \sin ^2 2 \theta\)
- D \(1+2 \sin ^2 \theta \cdot \cos ^2 \theta\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{4}(3+\cos 4 \theta)\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{cc}\cos ^2 \theta & -\sin ^2 \theta \\ \sin ^2 \theta & \cos ^2 \theta\end{array}\right| = \cos^2 \theta \cdot \cos^2 \theta - (-\sin^2 \theta) \cdot \sin^2 \theta\) \(= \cos^4 \theta + \sin^4 \theta\)
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