Question

The determinant $â\begin{array}{ccc}\cos (θ+Ï•)& −\sin (θ+Ï•)& \cos 2Ï•\\ \sin θ& \cos θ& \sin Ï•\\ −\cos θ& \sin θ& \cos Ï•\end{array}â$ is :

• A. 0
• B. independent of $θ$
• C. independent of $Ï•$
• D. independent of $θ$ \& $Ï•$ both

Answer 1

Answer: (B)

Directly open by $R_1$ to get
${\cos }^2(θ+ϕ)+{\sin }^2(θ+ϕ)+\cos 2ϕ$
$=1+\cos 2ϕ.\text{ Which is independent of }θ$