Question

If the determinant $\left| \begin{matrix} \cos 2x & \sin^{2}x & \cos 4x \\ \sin^{2}x & \cos 2x & \cos^{2}x \\ \cos 4x & \cos^{2}x & \cos 2x \end{matrix} \right|$ is expended in power of sin x. Then the constant term in the expansion is –

• A. 1
• B. 2
• C. –1
• D. None of these

Answer 1

Answer: (C)

–1

Answer 2

∆(x) = $\left| \begin{matrix} 1 - 2\sin^{2}x & \sin^{2}x & 1 - 8\sin^{2}x + 8\sin^{4}x \\ \sin^{2}x & 1 - 2\sin^{2}x & 1 - \sin^{2}x \\ 1 - 8\sin^{2}x + 8\sin^{4}x & 1 - \sin^{2}x & 1 - 2\sin^{2}x \end{matrix} \right|$

Put x = 0

∆(0) = $\left| \begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{matrix} \right|$ = –1