Question

If f(x) = `|(1 + sin^2x, cos^2x, 4 sin 2x),(sin^2x, 1 + cos^2x, 4 sin 2x),(sin^2 x, cos^2 x, 1 + 4 sin 2x)|` 

What is the maximum value of f(x)?

Options

• 2

• 4

• 6

• 8

Answer 1

6

Explanation:

f(x) = `|(1 + sin^2x, cos^2x, 4 sin 2x),(sin^2x, 1 + cos^2x, 4 sin 2x),(sin^2 x, cos^2 x, 1 + 4 sin 2x)|` 

Applying `C_1 rightarrow C_1 + C_2`

= `|(2, cos^2 θ, 4 sin 2x),(2, 1 + cos^2 θ, 4 sin 2x),(1, cos^2 θ, 1 + 4 sin 2x)|`

`("Applying"  R_2 rightarrow R_2 - R_1 and R_3 rightarrow R_3 - R_1)`

= `|(2, cos^2 θ, 4 sin 2x),(0, 1, 0),(-1, 0, 1)|`

f(x) = 2 + 4 sin 2x

∴ – 1 ≤ sin 2x ≤ 1, maximwn value of sin 2x = 1

Thus, maximwn value of f(x) = 2 + 4 = 6