First slide

Trigonometric equations

Question

The solution set of the equation $\tan (π \tan x) = \cot (π \cot x)$ is

Moderate

A

{ 0}
B

$\{π / 4\}$
C

$ϕ$
D

none of these

Solution

$\tan (π \tan x) = \tan (π / 2 - π \cot x)$
$\begin{array}{l} \Rightarrow π \tan x = π / 2 - π \cot x \Rightarrow \tan x + \cot x = 1 / 2 \\ \Rightarrow 2 \tan^{2} x - \tan x + 2 = 0 \\ \Rightarrow \tan x = \frac{1 + \sqrt{1 - 16}}{4} \end{array}$
which does not give real values of tan x.

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