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Question

If A2 + B2 + C2 = 0, then what is the value of the following?

\(\Delta = \begin{vmatrix} 1 & \cos C & \cos B \\\ \cos C & 1 & \cos A \\\ \cos B & \cos A & 1 \end{vmatrix}\)

This question was previously asked in
NDA 2 2025 GAT Question Paper (14-Sep-2025)
The correct answer is

1

From the matrix equation, the given values simplify to cosA = cosB = cosC = 1, which leads to value = 1.

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Important Questions from Complex Numbers

  1. If $\omega$ is a complex cube root of unity, then the value of $(1-\omega+\omega^2)(1-\omega^2+\omega^4)(1-\omega^4+\omega^8)$ is:
  2. If A + iB = tan (x + iy), then the value of tan 2x is?

  3. The value of \({\left( {\frac{{\cos \theta + i\sin \theta }}{{i\cos \theta + \sin \theta }}} \right)^4}\)  is:

  4. The smallest positive integer n for which \(\left(\dfrac{1+i}{1-i}\right)^n=1\) , is

  5. If ω is cube root of unity, then (3 + ω + 3ω 2) 6 is equal to

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