Answer:
Proved: [tex]c\sin A=a\sin C\Rightarrow \frac{\sin A}{a}=\frac{\sin C}{c}[/tex]
Step-by-step explanation:
Given: A triangle
To prove: [tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex]
Solution:
Trigonometry is a branch of mathematics that explains relationship between sides and angles of the triangle.
Sine of angle = side opposite to the angle / hypotenuse
In ΔADB,
[tex]\sin A=\frac{BD}{AB}=\frac{h}{c}\\\Rightarrow h=c\sin A\,\,\,(i)[/tex]
In ΔBDC,
[tex]\sin C=\frac{BD}{BC}=\frac{h}{a}\\\Rightarrow h=a\sin C\,\,\,(ii)[/tex]
From equations (i) and (ii),
[tex]c\sin A=a\sin C\\\frac{\sin A}{a}=\frac{\sin C}{c}[/tex]
Hence proved
