The minimum value of 27 tan^2 theta + 3 cot^2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) We use the Arithmetic Mean-Geometric Mean $(AM \geq GM)$ inequality,which states that for positive real numbers $a$ and $b$,$\frac{a+b}{2} \geq \s

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(B) We use the Arithmetic Mean-Geometric Mean $(AM \geq GM)$ inequality,which states that for positive real numbers $a$ and $b$,$\frac{a+b}{2} \geq \sqrt{ab}$.Let $a = 27 	an^2 	heta$ and $b = 3 \cot^2 	heta$.Then,$\frac{27 	an^2 	heta + 3 \cot^2 	heta}{2} \geq \sqrt{27 	an^2 	heta \cdot 3 \cot^2 	heta}$.$\frac{27 	an^2 	heta + 3 \cot^2 	heta}{2} \geq \sqrt{81 	an^2 	heta \cdot \cot^2 	heta}$.Since $	an 	heta \cdot \cot 	heta = 1$,we have:$\frac{27 	an^2 	heta + 3 \cot^2 	heta}{2} \geq \sqrt{81 \cdot 1}$.$\frac{27 	an^2 	heta + 3 \cot^2 	heta}{2} \geq 9$.$27 	an^2 	heta + 3 \cot^2 	heta \geq 18$.Thus,the minimum value is $18$.

The minimum value of $27 \tan^2 \theta + 3 \cot^2 \theta$ is

Similar Questions

If $A + B + C = \frac{3\pi}{2},$ then $\cos 2A + \cos 2B + \cos 2C = $

If $\alpha$ is the maximum value and $\beta$ is the minimum value of $\cos^2 \frac{x}{4} + \sin \frac{x}{4}$,$x \in R$,then $\alpha - \beta =$

The equation $(a + b)^2 = 4ab \sin^2 \theta$ is possible only when

The maximum value of $12 \sin x - 5 \cos x + 3$ is

Find the maximum and minimum values of the function given by $f(x) = |\sin 4x + 3|$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module