Question

The value of the determinant

D= $\left| \begin{matrix} a^{2} & a & 1 \\ \cos(nx) & \cos(n + 1)x & \cos(n + 2)x \\ \sin nx & \sin(n + 1)x & \sin(n + 2)x \end{matrix} \right|$is independent of –

• A. n
• B. a
• C. x
• D. None of these

Answer 1

Answer: (A)

n

Answer 2

D=a²[sin[(n+2)x–(n+1)x]]–a[sin[n + 2) x]

–(nx)]] +1.[sin[(n+1)x)–(nx)]]

 D = a² (sinx)–a.sin(2x)+sin (x)