Maximum value of the expression 1+sin2⁡xcos2⁡x4sin⁡2xsin2⁡x1+cos2⁡x4sin⁡2xsin2⁡xcos2⁡x1+4sin⁡2x= - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
4
B
6
C
2
D
-2

Solution:

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

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

Solution:

Related content