First slide

Trigonometric equations

Question

The number of solutions of $2 \sin^{2} \frac{x}{2} \sin^{2} x = x^{2} + \frac{1}{x^{2}}$ for $0 < x \leq \frac{π}{2}$

Easy

A

2
B

3
C

1
D

0

Solution

$x^{2} + \frac{1}{x^{2}} \geq 2 \Rightarrow R H S \geq 2$
But $L H S = 2 \sin^{2} \frac{x}{2} . \sin^{2} x < 2$
$∴$ given equation is not possible

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