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Question Number 33316 by rahul 19 last updated on 14/Apr/18
$${If}\:\:\frac{{f}\left(\mathrm{2}{x}+\mathrm{2}{y}\right)}{{f}\left(\mathrm{2}{x}−\mathrm{2}{y}\right)}\:=\:\frac{\mathrm{sin}\:\left({x}+{y}\right)}{\mathrm{sin}\:\left({x}−{y}\right)}\:. \\ $$$${Then}\:{find}\:{f}\left({x}\right)\:? \\ $$
Answered by MJS last updated on 14/Apr/18
$$\mathrm{2}{x}\pm\mathrm{2}{y}=\mathrm{2}\left({x}\pm{y}\right)=\mathrm{2}{p} \\ $$$${f}\left(\mathrm{2}{p}\right)=\mathrm{sin}\:{p}\:=\:\mathrm{sin}\:\left({x}\pm{y}\right) \\ $$$${f}\left({p}\right)=\mathrm{sin}\:\frac{{p}}{\mathrm{2}} \\ $$$${f}\left({x}\right)=\mathrm{sin}\:\frac{{x}}{\mathrm{2}} \\ $$
Commented by rahul 19 last updated on 14/Apr/18
$${thanks}! \\ $$