Question Number 193669 by Rupesh123 last updated on 17/Jun/23
Answered by AST last updated on 18/Jun/23
$${cos}\left({x}+{y}\right)+{isin}\left({x}+{y}\right)={e}^{{i}\left({x}+{y}\right)} ={e}^{{ix}} {e}^{{iy}} \\ $$$$=\left({cos}\left({x}\right)+{isin}\left({x}\right)\right)\left({cos}\left({y}\right)+{isin}\left({y}\right)\right) \\ $$$$={cos}\left({x}\right){cos}\left({y}\right)−{sin}\left({x}\right){cos}\left({y}\right)+{icos}\left({x}\right){sin}\left({y}\right)+{isin}\left({x}\right){cos}\left({y}\right) \\ $$$${Comparing}\:{real}\:{parts} \\ $$$$\Rightarrow{cos}\left({x}+{y}\right)={cos}\left({x}\right){cos}\left({y}\right)−{sin}\left({x}\right){cos}\left({y}\right) \\ $$
Commented by Rupesh123 last updated on 18/Jun/23
Perfect ��