اگر بدانیم $\operatorname{Cos}(\alpha +\beta )=\operatorname{Cos}(\alpha -\beta )$، حاصل $\operatorname{Sin}\alpha \operatorname{Sin}\beta $ کدام است؟
نکته: $\operatorname{Cos}(\alpha -\beta )=\operatorname{Cos}\alpha \operatorname{Cos}\beta +\operatorname{Sin}\alpha \operatorname{Sin}\beta $ و $\operatorname{Cos}(\alpha +\beta )=\operatorname{Cos}\alpha \operatorname{Cos}\beta -\operatorname{Sin}\alpha \operatorname{Sin}\beta $ با توجه به نکته میتوان نوشت: $\operatorname{Cos}(\alpha +\beta )=\operatorname{Cos}(\alpha -\beta )\Rightarrow \operatorname{Cos}\alpha \operatorname{Cos}\beta -\operatorname{Sin}\alpha \operatorname{Sin}\beta =\operatorname{Cos}\alpha \operatorname{Cos}\beta +\operatorname{Sin}\alpha \operatorname{Sin}\beta \Rightarrow 2\operatorname{Sin}\alpha \operatorname{Sin}\beta =0\Rightarrow \operatorname{Sin}\alpha \operatorname{Sin}\beta =0$