Question Number 10788 by okhema last updated on 25/Feb/17
$${factorise}\:{the}\:{expression}\:{sin}\mathrm{4}{x}−{sinx} \\ $$
Answered by argemiroQR last updated on 26/Feb/17
$${sin}\left(\mathrm{3}{x}+{x}\right)−{sinx}= \\ $$$${sin}\mathrm{3}{xcosx}+{cos}\mathrm{3}{xsinx}−{sinx}= \\ $$$${cosx}\left(\mathrm{3}{sinx}−\mathrm{4}{sin}^{\mathrm{3}} {x}\right)+\left({cos}^{\mathrm{3}} {x}−\mathrm{3}{cosx}\right){sinx}−{sinx}= \\ $$$$\mathrm{3}{sinxcosx}−\mathrm{4}{sin}^{\mathrm{3}^{} } {xcosx}+{sinxcos}^{\mathrm{3}} {x}−\mathrm{3}{sinxcosx}−{sinx}= \\ $$$${sinx}\left(\mathrm{3}{cosx}−\mathrm{4}{sin}^{\mathrm{2}} {xcosx}+{cos}^{\mathrm{3}} {x}−{cosx}−\mathrm{1}\right) \\ $$
Commented by okhema last updated on 27/Feb/17
$${i}\:{am}\:{last}\:{from}\:{the}\:{third}\:{line},{like}\:{you} \\ $$$${skip}\:{some}\:{steps} \\ $$