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Question Number 10788 by okhema last updated on 25/Feb/17
factorise the expression sin4x−sinx
$${factorise}\:{the}\:{expression}\:{sin}\mathrm{4}{x}−{sinx} \\ $$
Answered by argemiroQR last updated on 26/Feb/17
sin(3x+x)−sinx=  sin3xcosx+cos3xsinx−sinx=  cosx(3sinx−4sin^3 x)+(cos^3 x−3cosx)sinx−sinx=  3sinxcosx−4sin^3^  xcosx+sinxcos^3 x−3sinxcosx−sinx=  sinx(3cosx−4sin^2 xcosx+cos^3 x−cosx−1)
$${sin}\left(\mathrm{3}{x}+{x}\right)−{sinx}= \\ $$$${sin}\mathrm{3}{xcosx}+{cos}\mathrm{3}{xsinx}−{sinx}= \\ $$$${cosx}\left(\mathrm{3}{sinx}−\mathrm{4}{sin}^{\mathrm{3}} {x}\right)+\left({cos}^{\mathrm{3}} {x}−\mathrm{3}{cosx}\right){sinx}−{sinx}= \\ $$$$\mathrm{3}{sinxcosx}−\mathrm{4}{sin}^{\mathrm{3}^{} } {xcosx}+{sinxcos}^{\mathrm{3}} {x}−\mathrm{3}{sinxcosx}−{sinx}= \\ $$$${sinx}\left(\mathrm{3}{cosx}−\mathrm{4}{sin}^{\mathrm{2}} {xcosx}+{cos}^{\mathrm{3}} {x}−{cosx}−\mathrm{1}\right) \\ $$
Commented by okhema last updated on 27/Feb/17
i am last from the third line,like you  skip some steps
$${i}\:{am}\:{last}\:{from}\:{the}\:{third}\:{line},{like}\:{you} \\ $$$${skip}\:{some}\:{steps} \\ $$

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