cot^2 theta/ csc theta = cos theta times cot theta

Question

anonymous · Answer

whats the answer??? please help!!!!!

solomonzelman · Answer

$\Huge\color{green}{ \sf     \frac{cot^2θ}{cscθ} =cosθ \times cotθ }$

solomonzelman · Answer

we know that

$\Huge\color{red}{ \sf    cot^2x =\frac{cos^2x}{sin^2x} ~~~~~~~~~~ AND}$

$\Huge\color{red}{ \sf    cscx =\frac{1}{sinx}  }$


OK ?

anonymous · Answer

ok got it

solomonzelman · Answer

$\Huge\color{green}{ \sf     \frac{\frac{cos^2θ}{sin^2θ}}{\frac{1}{sinθ}} =cosθ \times cotθ }$

Now, I want to ask you to simplify the fraction on the left. It would be equal to ?

anonymous · Answer

uhhhhhhh yeah sin ^2 theta???? idk

anonymous · Answer

i really don't know csc?????

solomonzelman · Answer

HINT

$\Huge\color{green}{ \sf     \frac{\frac{S}{D}}{\frac{A}{B}} =\frac{S}{D} \div  \frac{A}{B}=\frac{S}{D} \times  \frac{B}{A}}$



$\Huge\color{green}{ \sf     \frac{\frac{cos^2θ}{sin^2θ}}{\frac{1}{sinθ}} =\frac{cos^2θ}{sin^2θ} \div  \frac{1}{sinθ}=\frac{cos^2θ}{sin^2θ}  \times  \frac{sinθ}{1} =?}$