First slide

Trigonometric equations

Question

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

Difficult

A

1
B

2
C

3
D

4

Solution

Given that $x^{2} - 3 [\sin (x - \frac{π}{6})] = 3$
Given equation can be written as $x^{2} - 3 = 3 [\sin (x - \frac{π}{6})]$
Hence, $x^{2} - 3 = - 3, 0, 3$
$\Rightarrow x = 0, x = \sqrt{3} is only solution$ $(i f x = - \sqrt{3} t h e n 0 = [\sin (x - \frac{π}{6})] \Rightarrow 0 \leq s i n (x - \frac{π}{6}) < 1, w h i c h i s n o t p o s i b l e f o r x = - \sqrt{3})$
similarly x= $\pm \sqrt{6}$ does not satisfy the equation

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