if cos theta = 3/ 4 , find the value of 9tan ^2 theta + 9
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Step-by-step explanation:
➡The minimum value of a tan2 θ + b cot2 θ 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 tan2 θ + 4 cot2 θ
Geometric mean = √(9 tan2θ × 4 cot2θ)
tan2θ = 1/cot2θ
So, Geometric mean = √(9 × 4) = 6
➡Minimum value = 2 × GM = 1
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