Minimum value of 12 cos2 alpha 3 sec2 alpha is ........

Quantitative Aptitude ( CCS) Trignometry

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Minimum value of 12 cos²α + 3 sec² α is

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Explanation:

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.