Answer:
See below
Step-by-step explanation:
It is a trigonometric identity that [tex]\frac{sin\theta}{cos\theta}=tan\theta[/tex].
Why is this the case? Let's think back to definitions:
[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]
[tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex]
[tex]tan\theta=\frac{opposite}{adjacent}[/tex]
So, [tex]\frac{sin\theta}{cos\theta}=\frac{\frac{opposite}{hypotenuse} }{\frac{adjacent}{hypotenuse} }=\frac{opposite}{hypotenuse}*\frac{hypotenuse}{adjacent}=\frac{opposite}{adjacent}=tan\theta[/tex].
