Cho tam giác ABC. Hãy chỉ ra hệ thức sai: cos(A + C)/2 = sin A/2

* Hướng dẫn giải

Đáp án B

$$\begin{gathered} \widehat{A}+\widehat{B}+\widehat{C}={180}^0 \\ \Rightarrow cos\frac{B+C}{2}=cos({90}^0-\frac{A}{2})=\sin \frac{A}{2} \end{gathered}$$

A đúng

$$\begin{gathered} \widehat{A}+\widehat{B}+\widehat{C}={180}^0 \\ \Rightarrow \sin \left(A+C\right)=\sin ({180}^0-B)=\sin B \end{gathered}$$

B sai

$$\begin{gathered} \widehat{A}+\widehat{B}+\widehat{C}={180}^0 \\ \Rightarrow cos\left(A+B+2C\right)=cos({180}^0+C)=-cosC \end{gathered}$$

C đúng

$$\begin{gathered} \widehat{A}+\widehat{B}+\widehat{C}={180}^0 \\ \Rightarrow cos\left(A+B\right)=cos({180}^0-C)=-cosC \end{gathered}$$

D đúng