The parameter on which the value of the determinant | , * 20 c 1&… - Vidyadip

MCQ

The parameter on which the value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&a&{{a^2}}\\{\cos (p - d)x}&{\cos px}&{\cos (p + d)x}\\{\sin (p - d)x}&{\sin px}&{\sin (p + d)x}\end{array}\,} \right|$ does not depend upon

A
$a$
✓
$p$
C
$d$
D
$x$

✓

Answer

Correct option: B.

$p$

b
(b) ${C_1} \to {C_1} + {C_3} - 2{C_2}$ $\cos dx$ gives
$\Delta = \left| {\,\begin{array}{*{20}{c}}{1 + {a^2} - 2a\cos dx}&a&{{a^2}}\\0&{\cos px}&{\cos (p + d)x}\\0&{\sin px}&{\sin (p + d)x}\end{array}\,} \right|$
=$(1 + {a^2} - 2a\cos dx)\sin dx$, (which is independent of $p$).

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