Answer:
[tex]\frac{b}{SinB}=\frac{SinA}{a}[/tex]
Step-by-step explanation:
Sine Rule = [tex]\frac{Sin A}{a} =\frac{Sin B}{b}=\frac{Sin C}{c}[/tex]
a)[tex]\frac{b}{SinB}=\frac{SinA}{a}[/tex]
Sine rule is [tex]\frac{Sin A}{a} =\frac{Sin B}{b}[/tex]
[tex]\frac{b}{Sin B} =\frac{a}{Sin A}[/tex]
Thus Option 1 cannot be derived from the law of sines
b)[tex]a\times sinB=b\times sinA[/tex]
Sine rule is [tex]\frac{Sin A}{a} =\frac{Sin B}{b}[/tex]
[tex]\frac{b}{Sin A} =\frac{a}{Sin B}[/tex]
Thus Option B can be derived from the law of sines.
c)[tex]\frac{Sin C}{SinA}=\frac{c}{a}[/tex]
Sine rule is [tex]\frac{Sin A}{a} =\frac{Sin C}{c}[/tex]
[tex]\frac{c}{a} =\frac{SinC}{Sin A}[/tex]
Thus Option C can be derived from the law of sines.
d)[tex]c \times sinA=a\times sinC[/tex]
Sine rule is [tex]\frac{Sin A}{a} =\frac{Sin C}{c}[/tex]
[tex]c \times sinA=a\times sinC[/tex]
Thus Option C can be derived from the law of sines.
Hence Option A cannot be derived from the law of sines
[tex]\frac{b}{SinB}=\frac{SinA}{a}[/tex]
