f4°F b+ g 02 +

1.	f4°F b+ g 02 +
Answer» The minimum value ofatan²θ +b cot²θ is 2√(ab) Here, a = 9 and b = 4 So, 2√(ab) = 2√(9×4) = 12 Arithmetic mean is always greater than or equal to geometric mean. AM ≥ GM or (a+b)/2≥ √(ab) Minimum value of a+b = 2√(ab) Arithmetic mean =9 tan^2θ + 4 cot^2θ Geometric mean =√(9tan^2θ × 4 cot^2θ) tan^2θ = 1/cot^2θ So, Geometric mean =√(9 × 4) = 6 Minimum value = 2× GM = 12 Wrong answer

Answer»

The minimum value ofatan²θ +b cot²θ is 2√(ab)

Here, a = 9 and b = 4

So, 2√(ab) = 2√(9×4) = 12

Arithmetic mean is always greater than or equal to geometric mean.

AM ≥ GM or (a+b)/2≥ √(ab)

Minimum value of a+b = 2√(ab)

Arithmetic mean =9 tan^2θ + 4 cot^2θ

Geometric mean =√(9tan^2θ × 4 cot^2θ)

tan^2θ = 1/cot^2θ

So, Geometric mean =√(9 × 4) = 6

Minimum value = 2× GM = 12

Wrong answer

Discussion