Answer:
[tex]\frac{c}{a}[/tex] and [tex]\frac{b}{a}[/tex]
Step-by-step explanation:
sinB = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{b}{a}[/tex]
tanC = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{c}{b}[/tex]
Thus
sinB tanC = [tex]\frac{b}{a}[/tex] × [tex]\frac{c}{b}[/tex] ( cancel b on numerator/ denominator )
= [tex]\frac{c}{a}[/tex]
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sinC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{c}{a}[/tex]
tanB = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{b}{c}[/tex]
Thus
sinC tanB = [tex]\frac{c}{a}[/tex] × [tex]\frac{b}{c}[/tex] ( cancel c on numerator/ denominator )
= [tex]\frac{b}{a}[/tex]
