Let ∆(x) = |1+ sin²x cos²x 4sin2x |
|sin²x 1+co²x 4sin2x |
|sin²x cos²x 1+4sin2x|

The value of x (0 ≤ x ≤ π/x) for which ∆(x) is maximum, is equal to
(a) π/2
(b) π/6
(c) π/3
(d) π/4

Step-by-step explanation:

The the value of x for which above determinant is maximum, is equals to

Given determinant is

We get,

We get,

We know,

So,

So, option (d) is correct.

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1. The determinant value remains unaltered if rows and columns are interchanged.

2. The determinant value is 0, if two rows or columns are identical.

3. The determinant value is multiplied by - 1, if successive rows or columns are interchanged.

4. The determinant value remains unaltered if rows or columns are added or subtracted.

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are