cho tam giác ABC cân tại A . tính P =Sin(AB,BC) + Sin(BC,CA) + Sìn(CA,AB) 15/08/2021 Bởi Adalynn cho tam giác ABC cân tại A . tính P =Sin(AB,BC) + Sin(BC,CA) + Sìn(CA,AB)
Đáp án: $\begin{array}{l}P = – \sin \widehat B – \sin \widehat C – \sin \widehat A\\ = – 2.\sin \widehat B – \sin \widehat A\\ = – 2.\sin \frac{{{{180}^0} – \widehat A}}{2} – \sin \widehat A\\ = – 2.\sin \left( {{{90}^0} – \frac{{\widehat A}}{2}} \right) – \sin \widehat A\\ = – 2.cos\frac{{\widehat A}}{2} – 2.sin\frac{{\widehat A}}{2}.cos\frac{{\widehat A}}{2}\\ = – 2cos\frac{{\widehat A}}{2}.\left( {1 + \sin \frac{{\widehat A}}{2}} \right)\end{array}$ Bình luận
Đáp án:
$\begin{array}{l}
P = – \sin \widehat B – \sin \widehat C – \sin \widehat A\\
= – 2.\sin \widehat B – \sin \widehat A\\
= – 2.\sin \frac{{{{180}^0} – \widehat A}}{2} – \sin \widehat A\\
= – 2.\sin \left( {{{90}^0} – \frac{{\widehat A}}{2}} \right) – \sin \widehat A\\
= – 2.cos\frac{{\widehat A}}{2} – 2.sin\frac{{\widehat A}}{2}.cos\frac{{\widehat A}}{2}\\
= – 2cos\frac{{\widehat A}}{2}.\left( {1 + \sin \frac{{\widehat A}}{2}} \right)
\end{array}$