Question

Let \( M \) and \( m \) respectively be the maximum and the minimum values of \[ f(x) = 1 + \sin^2 x \cos^2 x + \frac{4 \sin 4x}{\sin^2 x \cos^2 x} \] for \( x \in \mathbb{R} \). Then \( M^4 - m^4 \) is equal to:

• A. 1215
• B. 1040
• C. 1295
• D. 1280

Hint:

For functions involving trigonometric expressions, use trigonometric identities and calculus techniques to find extrema.

Answer 1

The Correct Option is D

- To solve this, we first find the maximum and minimum values of the function \( f(x) \) using trigonometric identities and optimization techniques. 
- After evaluating the maximum and minimum values, we calculate \( M^4 - m^4 \). 
- Thus, \( M^4 - m^4 = 1280 \).