Question

The minimum value of 27 tan2 + 3 cot2
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Answer 1

Answer:

sorry don't no the answer change the question

Answer 2

Answer:

Step-by-step explanation:

f(x)=27tan²x + 3cot²x

Consider the equation,

Arithmetic mean ≥ Geometric mean

(a+b)/2≥√(ab)

a + b ≥ 2√(ab)……(1)

Now consider the given function f(x) then,

f(x) = 27tan²x + 3cot²x

From the equation (1) now consider the given function f(x),

27tan²x + 3cot²x ≥ 2√[(27tan²x)(3cot²x)]

The expression in the LHS is simply a function f(x),

So,

f(x)≥2√(81(tan²x)(cot²x))

tanx = 1/cotx

Tanx.cotx = 1

f(x) ≥ 2√((81)(1))

f(x)≥ 2√(81)

f(x)≥2(9)

f(x)≥18

So the minimum value of given f(x) is 18.