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Question: In a quadrilateral ABCD, Let D = \(\left| \begin{matrix} \cos A & \sin A & \cos(A + D) \\ \cos B & ...

In a quadrilateral ABCD, Let D =

∣cos⁡Asin⁡Acos⁡(A+D)cos⁡Bsin⁡Bcos⁡(B+D)cos⁡Csin⁡Ccos⁡(C+D)∣\left| \begin{matrix} \cos A & \sin A & \cos(A + D) \\ \cos B & \sin B & \cos(B + D) \\ \cos C & \sin C & \cos(C + D) \end{matrix} \right| , then D is

A

Independent of A and B only

B

Independent of B and C only

C

Independent of A, B and C only

D

Independent of A, B, C and D all

Answer

Independent of A, B, C and D all

Explanation

Solution

C3 ® C3 – C1 cos D + C2 sin D = 0

So D = 0, hence D is independent of A, B, C, D all.