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Question

The parameter on which the value of the determinant ∣ ∣ ∣1aa2cos(pd)xcospxcos(p+d)xsin(pd)xsinpxsin(p+d)x∣ ∣ ∣ does not depend is ___

A
a
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B
p
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C
d
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D
x
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Solution

The correct option is B p
Expanding along first row, we have 1[cospx sin(p+d)xcos(p+d)x sinpx]
a[cos(pd)x sin(p+d)xcos(p+d)x sin(pd)x]
+a2[cos(pd)x sinpxcospx sin(pd)x]
=sindxasin2dx+a2 sindx
which is independent of p.

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