Question

$\left|\begin{array}{cc}{\sin }^2\theta & {\cos }^2\theta \\ {\cos }^2\theta & {\sin }^2\theta \end{array}\right|=$

• 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)

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