Question

The set of all values of a for which the function f(x)=(a²-3a+2)(cos²x/4-sin²x/4)+(a-1)x is decreasing is

• A. \([1,\infty)\)
• B. \((0,1)\cup(1,4)\)
• C. \((-2,4)\)
• D. (1,3)∪(3,5)

Hint:

A linear term dominates bounded trigonometric parts for monotonicity.

Answer 1

The Correct Option is A

Step 1: Differentiate: f'(x)=(a²-3a+2)·(bounded trig term)+(a-1)
Step 2: For f(x) to be decreasing for all x, require a-1\ge0.
Step 3: Hence a\ge1.