First slide

Trigonometric equations

Question

Total number of solutions for the equation is $x^{2} - 3 [\sin (x - \frac{π}{6})] = 3$ (where [.] denotes the greatest integer function)

Moderate

A

1
B

2
C

3
D

4

Solution

$W e h a v e x^{2} - 3 [\sin (x - \frac{π}{6})] = 3$
$W e c a n s e e t h a t \sin (x - \frac{π}{6}) \neq 1 \Rightarrow [\sin (x - \frac{π}{6})] = - 1 o r 0 (- 1 \leq \sin (x - \frac{π}{6}) < 1)$
$\Rightarrow T h e g i v e n e q u a t i o n b e c o m e s x^{2} + 3 = 3 o r x^{2} = 3 \Rightarrow x = 0, \sqrt{3} a r e t h e o n l y s o l u t i o n s s a t i s f y i n g t h e g i v e n e q u a t i o n$

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