Question

The determinant

$\left| \begin{matrix} \cos(\alpha + \beta) & –\sin(\alpha + \beta) & \cos 2\beta \\ \sin\alpha & \cos\alpha & \sin\beta \\ –\cos\alpha & \sin\alpha & \cos\beta \end{matrix} \right|$is independent of –

• A. a
• B. b
• C. a and b
• D. Neither a nor b

Answer 1

Answer: (A)

a

Answer 2

cos (a + b)[cosa cosb – sina sinb] +

sin (a + b) [sin a cos b + sin b cos a] +cos2b (sin²a + cos²a)

= [cos²(a + b) + sin²(a + b)] + cos2b

= 1 + cos2b

\ D is independent of a