$ \displaystyle \begin{array}{l}\sin (\alpha +\beta )=\sin \alpha \cos \beta +\cos \alpha \sin \beta ---(1)\\\\ \sin (\alpha -\beta )=\sin \alpha \cos \beta -\cos \alpha \sin \beta ---(2)\ \ \ \end{array}$
αိုαဲ့ Sum and Difference Formulae ေαြ αို αွα္αိαΎααα္ αα္αါαα္။
αီαွ်ျαα္း (1) αဲα (2) αို ေαါα္းαိုα္αα္...။
$ \displaystyle \sin (\alpha +\beta )+\ \sin (\alpha -\beta )=2\sin \alpha \cos \beta ---(*)$
αိုαΏαီး ααာαွာေαါ့...။
$ \displaystyle \alpha +\beta =\theta $ αဲα $ \displaystyle \alpha -\beta =\phi $ αိုα αားαိုα္αα္။
αါαိုαα္ $ \displaystyle \alpha =\frac{{\theta +\phi }}{2}$ αဲα $ \displaystyle \beta =\frac{{\theta -\phi }}{2}$ ျαα ္αြားαွာေαါ့...။
$ \displaystyle \alpha +\beta =\theta ,\ \alpha -\beta =\phi ,\ \ \alpha =\frac{{\theta +\phi }}{2},\beta =\frac{{\theta -\phi }}{2}$ αိုααို (*) αွာ α‘α ားαြα္းαိုα္αဲ့ α‘αါ αွာေαာ့ ေα‘ာα္αါ factor formula αို ααွိαွာ ျαα ္αါαα္။
| $ \displaystyle \sin \theta +\ \sin \phi =2\sin \frac{{\theta +\phi }}{2}\cos \frac{{\theta -\phi }}{2}$ |
αီαα ္αါ αီαွ်ျαα္း (1) αဲα (2) αို ႏႈα္αါαα္...။
$ \displaystyle \sin (\alpha +\beta )-\ \sin (\alpha -\beta )=2\cos \alpha \sin \beta $
α‘αα္αα‘αိုα္း αα္αိုα္αာαα္αိုးေαြ α‘α ားαြα္းαိုα္αα္ ...။
| $ \displaystyle \sin \theta -\ \sin \phi =2\cos \frac{{\theta +\phi }}{2}\sin \frac{{\theta -\phi }}{2}$ |
Identity αα ္αု αα္ααါαα္...။
ေαာα္αα္αီαွ်ျαα္း ႏွα ္αΎαာα္း αို αα္αΎαα့္αေα‘ာα္...။
$ \displaystyle \begin{array}{l} \cos (\alpha +\beta )=\cos \alpha \cos \beta -\sin \alpha \sin \beta ---(3)\\\\ \cos (\alpha -\beta )=\cos \alpha \cos \beta +\sin \alpha \sin \beta ---(4)\ \ \ \end{array}$
α‘αα္αါα‘αိုα္း αီα ွ်ျαα္း ႏွα ္ေαΎαာα္း (3) αဲα (4) αို ေαါα္းαα ္αွα့္ ႏႈα္αα ္αွα့္ αုα္αိုα္αα္ ...။
$ \displaystyle \begin{array}{l}(3)+(4)\Rightarrow \ \ \ \cos (\alpha +\beta )+\ \cos (\alpha -\beta )=2\cos \alpha \cos \beta \\\\(3)-(4)\Rightarrow \ \ \ \cos (\alpha +\beta )-\ \cos (\alpha -\beta )=-2\cos \alpha \cos \beta \end{array}$
α‘αα္αွာ αွာαဲ့αΏαီး ျαα ္αဲ့ $ \displaystyle \alpha +\beta =\theta ,\ \alpha -\beta =\phi ,\ \ \alpha =\frac{{\theta +\phi }}{2},\beta =\frac{{\theta -\phi }}{2}$ αိုααို αα္αိုα္αာ αα္αိုးေαြαွာ α‘α ားαြα္းαိုα္αα္...။
| $ \displaystyle \begin{array}{l}\cos \theta +\ \cos \phi =2\cos \displaystyle \frac{{\theta +\phi }}{2}\cos \displaystyle \frac{{\theta -\phi }}{2}\\\\\cos \theta -\ \cos \phi =-2\sin \displaystyle \frac{{\theta +\phi }}{2}\sin \displaystyle \frac{{\theta -\phi }}{2}\end{array}$ |
α
ာαα်αူ၏ α‘αြα်αို αေးα
ားα
ွာα
ောα့်αျှော်αျα်!
Post a Comment