First slide

Trigonometric equations

Question

$I f n b e t h e n u m b e r o f s o l u t i o n s o f t h e e q u a t i o n |\cot x| = \cot x + \frac{1}{\sin x} (0 < x < 2 π), t h e n n =$

Moderate

A

1
B

2
C

3
D

4

Solution

$|\cot x| = \{\begin{array}{l} - \cot x, \cot x < 0 \\ \cot x, \cot x \geq 0 \end{array}\}$
$C a s e (i) : L e t c o t x \geq 0 . T h e n c o t x = c o t x + \frac{1}{\sin x} \frac{1}{\sin x} = 0 \sin x = \infty w h i c h i s i m p o s s i b l e$
$C a s e (i i) : L e t c o t x < 0 . T h e n - c o t x = c o t x + \frac{1}{\sin x}$
$\Rightarrow \cos x = - \frac{1}{2} \Rightarrow x = \frac{2 π}{3}, \frac{4 π}{3} (∵ 0 < x < 2 π) \Rightarrow x = \frac{2 π}{3} (∵ o n l y c o t x < 0 h a s s o l u t i o n)$

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