Giải thích các bước giải:

$\begin{array}{l}
d)2{R^2}\sin A\sin B\sin C\\
 = 2\left( {R\sin A} \right)\left( {R\sin B} \right)\sin C\\
 = 2\left( {\dfrac{1}{2}a} \right)\left( {\dfrac{1}{2}b} \right)\sin C\\
 = \dfrac{1}{2}ab\sin C\\
 = S\\
e)\dfrac{1}{2}\sqrt {{{\overrightarrow {AB} }^2}{{\overrightarrow {AC} }^2} - {{\left( {\overrightarrow {AB} \overrightarrow {AC} } \right)}^2}} \\
 = \dfrac{1}{2}\sqrt {A{B^2}A{C^2} - A{B^2}A{C^2}{{\cos }^2}A} \\
 = \dfrac{1}{2}\sqrt {A{B^2}A{C^2}\left( {1 - {{\cos }^2}A} \right)} \\
 = \dfrac{1}{2}\sqrt {A{B^2}A{C^2}{{\sin }^2}A} \\
 = \dfrac{1}{2}AB.AC.\sin A\\
 = S\\
f)b\cos C + c\cos B\\
 = 2R\sin B\cos C + 2R\sin C\cos B\\
 = 2R\left( {\sin B\cos C + \sin C\cos B} \right)\\
 = 2R\sin \left( {B + C} \right)\\
 = 2R\sin A\\
 = a\\
g)\dfrac{2}{{bc}}\sqrt {p\left( {p - a} \right)\left( {p - b} \right)\left( {p - c} \right)} \\
 = \dfrac{2}{{bc}}.S\\
 = \dfrac{{2S}}{{bc}}\\
 = \sin A\\
h)4\left( {m_a^2 + m_b^2 + m_c^2} \right)\\
 = 4\left( {\dfrac{{2\left( {{b^2} + {c^2}} \right) - {a^2}}}{4} + \dfrac{{2\left( {{a^2} + {c^2}} \right) - {b^2}}}{4} + \dfrac{{2\left( {{a^2} + {b^2}} \right) - {c^2}}}{4}} \right)\\
 = 2\left( {{b^2} + {c^2}} \right) - {a^2} + 2\left( {{a^2} + {c^2}} \right) - {b^2} + 2\left( {{a^2} + {b^2}} \right) - {c^2}\\
 = 3\left( {{a^2} + {b^2} + {c^2}} \right)\\
i)\sin B\cos C + \sin C\cos B\\
 = \sin \left( {B + C} \right)\\
 = \sin A\\
j)2R\sin B\sin C\\
 = b\sin C\\
 = {h_a}
\end{array}$