Question

What is the minimum value of 12cos²a + 3 sec²a?​

Answer 1

Answer:

Let A = 12cos2α + 3 sec2α

⇒ A = 3(4 cos2α + sec2α)

⇒ A = 3[(2 cos α – sec α)2 + 4]

⇒ A = 3(2 cos α – sec α)2 + 12

For minimum value of A, 2008α – sec α = 0

2 cos α = sec α

Hence, the minimum value of the expression = 12.