Question

simplify sinx+cosx=(sinx/1-(cosx/sinx))+(cosx/1-(sinx/cosx))

Answer 1

You mean prove the identity?

Answer 2

Are you sure about the parts which say sinx/1 and cosx/1? Aren't they just sinx and cosx respectively?

Answer 3

verify that it is an identity

Answer 4

\[\sin(x)+\cos(x)=\frac{\sin(x)}{1-\frac{\cos(x)}{\sin(x)}}+\frac{\cos(x)}{1-\frac{\sin(x)}{\cos(x)}}\]?

Answer 5

yes

Answer 6

I would take the ugly side and tried to show it is the prettier side

Answer 7

Get rid of the compound fractions on the right hand side

Answer 8

I've tried that and i can't get them to equal out

Answer 9

You have two terms.

Both terms are fractions.

Both fractions contain fractions. (compound fractions they are)

Multiply both fractions be a certain 1 that will clear the "compoundedness".

Answer 10

what?

Answer 11

Do you have a question?

I'm asking you to make the compound fractions into regular fractions.

Answer 12

i did that

Answer 13

\[\frac{\sin(x)}{1-\frac{\cos(x)}{\sin(x)}} \cdot 1+\frac{\cos(x)}{1-\frac{\sin(x)}{\cos(x)}} \cdot 1 \]
What kinda 1 should you choose for the first 1?
What kinda 1 should you choose for the second 1?

Answer 14

Can you answer these questions?

Answer 15

ya

Answer 16

Ok so what did you choose for the 1st 1 and 2nd 1?

Answer 17

\[\frac{ \sin^2x }{1-cosx ? }\]

Answer 18

Ok I will tell you this step
For the 1st 1 I chose the 1 to be sin(x)/sin(x)
For the 2nd 1 I chose the 1 to be cos(x)/cos(x)
So like this we have:
\[\frac{\sin(x)}{1-\frac{\cos(x)}{\sin(x)}} \cdot \frac{\sin(x)}{\sin(x)}+\frac{\cos(x)}{1-\frac{\sin(x)}{\cos(x)}} \cdot \frac{\cos(x)}{\cos(x)}\]

Answer 19

So we have:
\[\frac{\sin(x) \cdot \sin(x)}{(1-\frac{\cos(x)}{\sin(x)})(\sin(x))}+\frac{\cos(x) \cdot \cos(x)}{(1-\frac{\sin(x)}{\cos(x)} ) (\cos(x))}\]

Answer 20

Recall the distributive property a(b+c)=ab+ac
Use this here on the bottoms for sure
And you should be able to multiply the tops with no problems

Answer 21

@karr Where did you go? :(

Answer 22

sorry. okay i got that.. the top of the fractions equal 1 now....

Answer 23

??