First slide

Trigonometric equations

Question

Number of solutions of the equation $\sin (\frac{π x}{2 \sqrt{3}}) = x^{2} - 2 \sqrt{3} x + 4$ is

Easy

A

0
B

1
C

2
D

4

Solution

We have $\sin (\frac{π x}{2 \sqrt{3}}) = x^{2} - 2 \sqrt{3} x + 4$ $= {(x - \sqrt{3})}^{2} + 1$
$\Rightarrow L H S \leq 1, R H S \geq 1$
$\Rightarrow L H S = R H S = 1$
$\Rightarrow x = \sqrt{3}$

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