The number of values of a for which the function f(x) = cos2x + 2a(1 + cosx) has a minimum value of 1/2 is
(A) 0 (B) 1 (C) 2 (D) 3
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Answer:
(B)1
Step-by-step explanation:
f(x) = 2 cos2 x – 1 + 2a + 2a cos x
= 2 cos2 x + 2a cos x + 2a –1
min f(x) =1/2
min (2 cos2x + 2a cos x + 2a –1) =1/2
min (2t2 + 2at + 2a –1) =1/2
where t ∈[–1, 1]
now take cases
Case-I –1 ≤-1/2a≤1
case 2 -1/2a>1
Case 3 -1/2a<1
Option (B) is correct
https://www.resonance.ac.in/answer-key-solutions/NMTC/2019/Stage-1/Solutions/Inter-v3.pdf
you can refer the third question in this for answer
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