prove the identity is true (1-cos^2x)cotx=sinxcosx

Question

mathlegend · Answer

Hi, do you have an identity sheet that has Pythagorean identities on it?

mathlegend · Answer

Can you tell me what $$1-\cos ^{2}x $$ equals?

mathlegend · Answer

@hconejo100

anonymous · Answer

sin^2x

mathlegend · Answer

and what does cotx also equal is it... $$\frac{ cosx }{ sinx }$$ ?

anonymous · Answer

yes

mathlegend · Answer

So lets see what we have...

mathlegend · Answer

$$\sin ^{2}x(\frac{ cosx }{ sinx })$$

mathlegend · Answer

which simplifies to... $$\frac{ \sin ^{2}xcosx }{ sinx } = sinxcosx$$

mathlegend · Answer

Make sense?

anonymous · Answer

not really

mathlegend · Answer

What step does not make sense?

anonymous · Answer

well it does makes sense but on my homework i have to prove it by writing it step by step and what rule is each step

mathlegend · Answer

$$1 - \cos ^{2}x = \sin ^{2}x$$
is substitution

mathlegend · Answer

$$cotx = \frac{ cosx }{ sinx }$$

Substitution

mathlegend · Answer

$$\sin ^{2}x(\frac{ cosx }{ sinx })$$

Multiplication

mathlegend · Answer

$$\frac{ \sin ^{2}xcosx }{ sinx } = sinxcosx$$

Simplifying

mathlegend · Answer

better @hconejo100 ?

anonymous · Answer

the rules i can chose from are 
-algebra 
-reciprocal 
-quotient
-Pythagorean
-odd/even
here is an example my teacher gave me cotx/cscx-1=cscx+1/cotx
to prove it he put 
=cotx/cscx-1*cscx+1/cscx+1   Algebra 
=cotx(cscx+1)/csc^2x-1           Algebra 
=cotx(cscx+1)/cot^2x               Pythagorean
=cscx+1/cotx                           algebra

mathlegend · Answer

1st = Pythagorean
2nd = Reciprocal
3rd =Algebra
4th = Quotient

anonymous · Answer

thanks for your help