Prove (cotØ+1)/ cscØ = cosØ + sinØ

Question

solomonzelman · Answer

can you work on both sides, or work only with one side ?

anonymous · Answer

only one

solomonzelman · Answer

$\LARGE\color{blue}{ \bf      \frac{cotØ+1}{cscØ}=cosØ+sinØ	 }$

being that  cscØ=1/sinØ  therefore  1/cscØ = 1/(1/sinØ)=sinØ     So...

$\LARGE\color{blue}{ \bf      (cotØ+1)sinØ=cosØ+sinØ	 }$

so far so good ?

anonymous · Answer

yes it is good

solomonzelman · Answer

So right now we have,

$\LARGE\color{blue}{ \bf      (cotØ+1)sinØ=cosØ+sinØ	 }$  lets expand the left side,
$\LARGE\color{blue}{ \bf      cotØ~sinØ~+sinØ=cosØ+sinØ	 }$

Now,  cotØ =cos Ø/ sinØ

So, substituting    cos Ø/ sinØ    instead of   cotØ

$\LARGE\color{blue}{ \bf      \frac{cosØ  }{sinØ} ~sinØ~+sinØ=cosØ+sinØ	 }$

now the sines in the fraction cancel,

$\LARGE\color{blue}{ \bf      \frac{cosØ  }{\cancel{ sinØ} } ~\cancel{ sinØ} ~+sinØ=cosØ+sinØ	 }$


need more help ?

anonymous · Answer

wow that looks like 10  times better than what i was trying to do, thanks so much!!!

solomonzelman · Answer

Anytime, BTW you are yellow now :)

anonymous · Answer

Aww thanks!!