Question

Determinant $\left| \begin{matrix} 1 & x & y \\ 2 & \sin x + 2x & \sin y + 2y \\ 3 & \cos x + 3x & \cos y + 3y \end{matrix} \right|$ is equal to

• A. sin (x – y)
• B. cos (x – y)
• C. cos (x + y)
• D. xy sin (x – y)

Answer 1

Answer: (A)

sin (x – y)

Answer 2

R₂ → R₂ – 2R₁, R₃ → R₃ – 3R₁

∆ = $\left| \begin{matrix} 1 & x & y \\ 0 & \sin x & \sin y \\ 0 & \cos x & \cos y \end{matrix} \right|$ = sin x cos y – cos x sin y

= sin (x – y)