The product of sin B and tan C is c/a
The product of sin C and tan B is b/a
Further explanation
We can use
SOH stands for Sine = Opposite ÷ Hypotenuse.
CAH stands for Cosine = Adjacent ÷ Hypotenuse.
TOA stands for Tangent = Opposite ÷ Adjacent.
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[tex]\tt sin~B=\dfrac{b}{a}\\\\Tan~C=\dfrac{c}{b}\\\\sin~B\times Tan~C=\dfrac{b}{a}\times \dfrac{c}{b}=\dfrac{c}{a}[/tex]
[tex]\tt sin~C=\dfrac{c}{a}\\\\Tan~B=\dfrac{b}{c}\\\\sin~C\times tan~B=\dfrac{c}{a}\times \dfrac{b}{c}=\dfrac{b}{a}[/tex]
