what is tan theta over sec theta expressed in sin theta

Question

solomonzelman · Answer

$\Huge\color{blue}{ \sf     \frac{Tanθ}{Secθ} }$

I'll post 2 rules below (in red) that I'll have to use.

$\Huge\color{red}{ \sf     Tanθ= \frac{Sinθ}{Cosθ} }$

$\Huge\color{red}{ \sf     Secθ= \frac{1}{Cosθ} }$


So lets substitute...

$\Huge\color{blue}{ \sf     \frac{Tanθ}{Secθ}~~-> }$    $\Huge\color{blue}{ \sf     \frac{\frac{Sinθ}{Cosθ}}{\frac{1}{Cosθ}} }$

Now solving further

$\Huge\color{blue}{ \sf     \frac{\frac{Sinθ}{Cosθ}}{\frac{1}{Cosθ}}  ~~~-> }$   $\Huge\color{blue}{ \sf     \frac{Sinθ}{Cosθ} \div \frac{1}{Cosθ}~~-> }$ 


 $\Huge\color{blue}{ \sf     \frac{Sinθ}{Cosθ} \times\frac{Cosθ}{1}~~-> }$ 

 $\Huge\color{blue}{ \sf     \frac{Sinθ}{1} ~~->~~Sinθ }$