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Question: The solution of the equation \(\left| \begin{matrix} \cos\theta & \sin\theta & \cos\theta \\ - \sin...

The solution of the equation $\left| \begin{matrix} \cos\theta & \sin\theta & \cos\theta \

  • \sin\theta & \cos\theta & \sin\theta \
  • \cos\theta & - \sin\theta & \cos\theta \end{matrix} \right| = 0,$ is
A

θ=nπ\theta = n\pi

B

θ=2nπ±π2\theta = 2n\pi \pm \frac{\pi}{2}

C

θ=nπ±(−1)nπ4\theta = n\pi \pm ( - 1)^{n}\frac{\pi}{4}

D

θ=2nπ±π4\theta = 2n\pi \pm \frac{\pi}{4}

Answer

θ=2nπ±π2\theta = 2n\pi \pm \frac{\pi}{2}

Explanation

Solution

After solving the determinant 2cos⁡θ=0⇒θ=2nπ±π2.2\cos\theta = 0 \Rightarrow \theta = 2n\pi \pm \frac{\pi}{2}.