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