1.

The least value of sin2x-√3cot2x

Answer»

Step-by-step explanation:

What is the minimum value of 3tan^2x+12cot^2x?

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For these questions you can go by concept of maxima and minima in calculus …

But still there's a more EASY way which is known as AM GM inequality and it states that if there are TWO positive reals say a and b then their arithmetic mean is greater than or equal to their geometric mean … (Seems complex right but It's not at all!)

Mathematically (a+b)/2 >( or equal to) root(a.b)

for this question let's take the two terms individually then apply AM GM inequality

(3tan^2x + 12/tan^2x)/2 > root (3tan^2x . 12/tan^2x)

The tan^2x expression under the radical is cancelled and you get finally

3tan^2x+12/tan^2x > 2.root 36

Which shows that 3tan^2x+12/tan^2x > 12

So minimum possible value is 12

Note: “>” sign USED here represents greater than or equal to


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