Q6 of 256 Page 7

Mark the correct alternative in the following:

The value of the determinant is independent of


Let us solve the determinant.


We know that,


Determinant of 3 × 3 matrix is given as,




So,




By trigonometric identity, we have


sin (α – β) = sin α cos β – cos α sin β


So, we can write





Note that, the result has ‘a’ as well as ‘x’, but doesn’t contain ‘n’.


Thus, the determinant is independent of n.

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