Question Number 120393 by help last updated on 31/Oct/20
Commented by help last updated on 31/Oct/20
pls how to prove the identity?
Commented by $@y@m last updated on 31/Oct/20
$${Please}\:{type}\:{the}\:{question}. \\ $$
Commented by help last updated on 31/Oct/20
$${sinA}+{sinB}+{sinC}−\left({sinA}+{B}+{C}\right)=?? \\ $$$$ \\ $$
Commented by $@y@m last updated on 31/Oct/20
$$=\mathrm{2sin}\:\frac{{A}+{B}}{\mathrm{2}}\mathrm{cos}\:\frac{{A}−{B}}{\mathrm{2}}+\mathrm{2cos}\:\frac{{A}+{B}+\mathrm{2}{C}}{\mathrm{2}}\mathrm{sin}\:\frac{−{A}−{B}}{\mathrm{2}} \\ $$$$=\mathrm{2sin}\:\frac{{A}+{B}}{\mathrm{2}}\left\{\mathrm{cos}\:\frac{{A}−{B}}{\mathrm{2}}−\mathrm{cos}\:\frac{{A}+{B}+\mathrm{2}{C}}{\mathrm{2}}\right\} \\ $$$$=\mathrm{2sin}\:\frac{{A}+{B}}{\mathrm{2}}.\mathrm{2sin}\:\:\frac{{A}+{C}}{\mathrm{2}}\mathrm{sin}\:\frac{{B}+{C}}{\mathrm{2}} \\ $$