5. The sum of the extremum values of sin2 x + 2 sin x + 3 is:
1) 8 2) 6 3) 4 4) 2
Ans: (3)
Sol: sin2 x + 2 sin x + 3 = (1 + sin x)2 + 2
-1 ≤ sin x ≤ 1
0 ≤ 1 + sin x ≤ 2
0 ≤ (1 + sin x)2≤ 4
2 ≤ (1 + sin x)2≤ 6
2 ≤ (sin2 x + 2 sin x + 3) ≤ 6
... Sum of extremum values = 2 + 6 = 8
