Review question

# If $R$ is the circumradius of triangle $ABC$, can we show $a\:/\sin A = 2R$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5988

## Question

With the usual notation prove that $\begin{equation*} \frac{a}{\sin A} = 2R \end{equation*}$

where $R$ is the radius of the circumcircle of the triangle $ABC$.

[You need consider only the case when the angle $A$ is acute.]

Hence or otherwise deduce that

1. $a \cos A + b \cos B = c \cos (A-B)$,
2. $a \cos A + b \cos B + c \cos C = 4 R \sin A \sin B \sin C$.