Question

$\begin{vmatrix}\sin ^{2} \theta & \cos ^{2} \theta \\ \cos ^{2} \theta & \sin ^{2} \theta\end{vmatrix}=$

• A. $\cos 2 \theta$
• B. $\frac{1}{2}\left(1+\cos ^{2} 2 \theta\right)$
• C. $\frac{1}{2}\left(1-\sin ^{2} 2 \theta\right)$
• D. $\frac{1}{2} \sin ^{2} 2 \theta$

Answer 1

Answer: (B)

$\sin ^{4} \theta+\cos ^{4} \theta=1-2 \sin ^{2} \theta \cos ^{2} \theta$
$=1-\frac{1}{2} \sin ^{2} 2 \theta=1-\frac{1}{2}\left(1-\cos ^{2} 2 \theta\right)$
$=\frac{1}{2}\left(1+\cos ^{2} 2 \theta\right)$