Question Number 152035 by puissant last updated on 25/Aug/21
$${Show}\:{that}\:\mathrm{2}{sin}\mathrm{7}\theta{cos}\mathrm{3}\theta={sin}\mathrm{10}\theta+{sin}\mathrm{4}\theta. \\ $$
Answered by som(math1967) last updated on 25/Aug/21
$$\mathrm{2}{sinA}\boldsymbol{{cosB}}=\boldsymbol{{sin}}\left(\boldsymbol{{A}}+\boldsymbol{{B}}\right)+\boldsymbol{{sin}}\left(\boldsymbol{{A}}−\boldsymbol{{B}}\right) \\ $$$$\therefore\mathrm{2}\boldsymbol{{sin}}\mathrm{7}\boldsymbol{\theta{cos}}\mathrm{3}\boldsymbol{\theta}=\boldsymbol{{sin}}\left(\mathrm{7}\boldsymbol{\theta}+\mathrm{3}\boldsymbol{\theta}\right)+\boldsymbol{{sin}}\left(\mathrm{7}\boldsymbol{\theta}−\mathrm{3}\boldsymbol{\theta}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\boldsymbol{{sin}}\mathrm{10}\boldsymbol{\theta}+{s}\boldsymbol{{in}}\mathrm{4}\boldsymbol{\theta} \\ $$
Commented by puissant last updated on 25/Aug/21
$${thank}\:{you}\:{sir}.. \\ $$