Maximum value of the expression 1+sin2⁡xcos2⁡x4sin⁡2xsin2⁡x1+cos2⁡x4sin⁡2xsin2⁡xcos2⁡x1+4sin⁡2x=

# Maximum value of the expression $\left|\begin{array}{ccc}1+{\mathrm{sin}}^{2}\mathrm{x}& {\mathrm{cos}}^{2}\mathrm{x}& 4\mathrm{sin}2\mathrm{x}\\ {\mathrm{sin}}^{2}\mathrm{x}& 1+{\mathrm{cos}}^{2}\mathrm{x}& 4\mathrm{sin}2\mathrm{x}\\ {\mathrm{sin}}^{2}\mathrm{x}& {\mathrm{cos}}^{2}\mathrm{x}& 1+4\mathrm{sin}2\mathrm{x}\end{array}\right|=$

1. A

4

2. B

6

3. C

2

4. D

-2

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

Let $\mathrm{f}\left(\mathrm{x}\right)=\left|\begin{array}{ccc}1+{\mathrm{sin}}^{2}\mathrm{x}& {\mathrm{cos}}^{2}\mathrm{x}& 4\mathrm{sin}2\mathrm{x}\\ {\mathrm{sin}}^{2}\mathrm{x}& 1+{\mathrm{cos}}^{2}\mathrm{x}& 4\mathrm{sin}2\mathrm{x}\\ {\mathrm{sin}}^{2}\mathrm{x}& {\mathrm{cos}}^{2}\mathrm{x}& 1+4\mathrm{sin}2\mathrm{x}\end{array}\right|\begin{array}{r}{\mathrm{R}}_{2}\to {\mathrm{R}}_{2}-{\mathrm{R}}_{1}\\ {\mathrm{R}}_{3}\to {\mathrm{R}}_{3}-{\mathrm{R}}_{1}\end{array}$
$\begin{array}{l}\mathrm{f}\left(\mathrm{x}\right)=\left|\begin{array}{ccc}1+{\mathrm{sin}}^{2}\mathrm{x}& {\mathrm{cos}}^{2}\mathrm{x}& 4\mathrm{sin}2\mathrm{x}\\ -1& 1& 0\\ -1& 0& 1\end{array}\right|\\ \mathrm{f}\left(\mathrm{x}\right)=\left(1+{\mathrm{sin}}^{2}\mathrm{x}\right)\left(1\right)-{\mathrm{cos}}^{2}\mathrm{x}\left(-1\right)+4\mathrm{sin}2\mathrm{x}\left(0+1\right)\\ =1+{\mathrm{sin}}^{2}\mathrm{x}+{\mathrm{cos}}^{2}\mathrm{x}+4\mathrm{sin}2\mathrm{x}\\ =1+1+4\mathrm{sin}2\mathrm{x}\\ =2+4\mathrm{sin}2\mathrm{x}\end{array}$
Maximum value of $\mathrm{f}\left(\mathrm{x}\right)=2+4\left(1\right)=2+4=6$

## Related content

 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formulae Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics  +91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)