Discussion

Explanation:

The set of all real value of p for which the equation 3sin²x + 12cosx – 3 = p has one solution is

Given, 3sin²x + 12cosx – 3 = p
⇒ 3(1 - cos²x) + 12cosx – 3 = p
⇒ -3cos²x + 12cosx – p = 0
⇒ -3[cos²x - 4cosx] – p = 0
⇒ -3[cos²x - 4cosx + 4] + 12 – p = 0 [Adding and subtracting 12]
⇒ -3[cosx - 2]² = p - 12
⇒ [cosx - 2]² = -p/3 + 4

Now, 1 ≥ cosx ≥ -1
∴ 9 ≥ (cosx - 2)² ≥ 1
⇒ 9 ≥ -p/3 + 4 ≥ 1
⇒ 5 ≥ -p/3 ≥ -3
⇒ -15 ≤ p ≤ 9

Hence, option (c).

» Your doubt will be displayed only after approval.