First slide

Extreme values and Periodicity of Trigonometric functions

Question

If $a \tan α + \sqrt{a^{2} - 1} \tan β + \sqrt{a^{2} + 1} \tan γ = 2 a,$ where a is constant and $α, β, γ$ are variable angles then the least value of
$3 (\tan^{2} α + \tan^{2} β + \tan^{2} γ)$

Moderate

A

4.00
B

1
C

2
D

3

Solution

Let $\bar{A} = a \bar{i} + \sqrt{a^{2} - 1} \bar{j} + \sqrt{a^{2} + 1} \bar{k}$
$\vec{B} = \tan α \vec{i} + \tan β \vec{j} + \tan γ \bar{k} \Rightarrow \bar{A} . \bar{B} = 2 a$
$\Rightarrow {| \bar{A} |}^{2} {| \bar{B} |}^{2} \cos^{2} θ = 4 a^{2}$
$3 [\tan^{2} α + \tan^{2} β + \tan^{2} γ] \geq 4$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App