Question Number 17153 by Tinkutara last updated on 01/Jul/17
![If m, n ∈ N(n > m), then number of solutions of the equation n∣sin x∣ = m∣sin x∣ in [0, 2π] is](https://www.tinkutara.com/question/Q17153.png)
$$\mathrm{If}\:{m},\:{n}\:\in\:{N}\left({n}\:>\:{m}\right),\:\mathrm{then}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${n}\mid\mathrm{sin}\:{x}\mid\:=\:{m}\mid\mathrm{sin}\:{x}\mid\:\mathrm{in}\:\left[\mathrm{0},\:\mathrm{2}\pi\right]\:\mathrm{is} \\ $$
Answered by mrW1 last updated on 01/Jul/17
$${n}\mid\mathrm{sin}\:{x}\mid\:=\:{m}\mid\mathrm{sin}\:{x}\mid \\ $$$$\because\:\mathrm{m}\neq\mathrm{n} \\ $$$$\therefore\:\mid\mathrm{sin}\:\mathrm{x}\mid=\mathrm{0} \\ $$$$\mathrm{x}=\mathrm{0},\pi,\mathrm{2}\pi \\ $$$$\Rightarrow\mathrm{there}\:\mathrm{are}\:\mathrm{3}\:\mathrm{solutions} \\ $$
Commented by Tinkutara last updated on 02/Jul/17
$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$