Question

The value of $\left|\begin{array}{ccc}cos(\theta +\propto )& -sin(\theta +\propto )& cos2\propto \\ sin\theta & cos\theta & sin\propto \\ -cos\theta & sin\theta & \lambda cos\propto \end{array}\right|$ is

• A. independent of $\theta$ for all $\lambda ϵR$
• B. Independent of $\theta$ and $\propto$ for $\lambda =1$
• C. independent of $\lambda$ for all $\theta ϵR$
• D. Independent of $\theta$ and $\propto$ for $\lambda =-1$

Answer 1

Answer: (A), (D)

The correct options are
A

independent of $\theta$ for all $\lambda ϵR$

D

Independent of $\theta$ and $\propto$ for $\lambda =-1$

Given det $=(\lambda +1)co{s}^2\propto$