Question Number 17153 by Tinkutara last updated on 01/Jul/17 | ||
$$\mathrm{If}\:{m},\:{n}\:\in\:{N}\left({n}\:>\:{m}\right),\:\mathrm{then}\:\mathrm{number}\:\mathrm{of} \\ $$ $$\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$ $${n}\mid\mathrm{sin}\:{x}\mid\:=\:{m}\mid\mathrm{sin}\:{x}\mid\:\mathrm{in}\:\left[\mathrm{0},\:\mathrm{2}\pi\right]\:\mathrm{is} \\ $$ | ||
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 byTinkutara last updated on 02/Jul/17 | ||
$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$ | ||