Trying to solve a trig identity problem: sin x +1/ cos x + cot x.... I worked it almost to the end and my result was : sin x + sin ^2x / (sin x)(cos x) + cos x... Can any one help me?

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Trying to solve a trig identity problem: sin x +1/ cos x + cot x.... I worked it almost to the end and my result was : sin x + sin ^2x / (sin x)(cos x) + cos x... Can any one help me?

Mathematics
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Where is the = sign?
oh sorry i forgot... = tan sin x + 1 / cos x + cot x = tan x
What did you do first?

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The first step I did was change the cot in denominator into cos and sin
After I did that then I precedded with 1+ sin x/ (sin x)(cos x) + cos x/ sin
Tell me in the original problem. is sin x by itself and then 1/cosx by itself and then cotx by itself....
Ok, the original problem : (sin x +1) / (cos x + cot x) = tan x
Oh.. ok then just a minute.
Here is what to do.. let me know if you are following me. In algebra when you have a denominator and you are solving you usually multiply by the denominator so you can get rid of the denominator. So. I am going to multiply both sides by (cos x + cot x).. If you do you get (sin x + 1) = tan x(cos x + cot x) OK?
I don't follow... i thoght you multiply by the reciprocal..
i have to work on one side to equal the other side, which is tan x
(cos x + cot x) times (sin x + 1) /(cos x + cot x) = tan x (cos x + cot x) The (cos x + cot x) would cancel out on the left hand side. It is legal to multiply both sides by the same thing.
In math, you don't have to just work on one side. If you want to do it your way. give me a second. It is very easy if you do it my way... but just a second and I will get back with you shortly.
Yes, it is legal to do both sides, however my professor wants us to work it by choosing complex side to prove other side
It is WAY to messy to try and even get it your way.... if you had x/3 + 1/5 = 10 You should have been taught to get the common denominator of 15 and multiply every term by 15 which would give you 15 * (x/3) + 15 * (1/5) = 10 * 15 Do you remember doing this? It gets rid of the denominators for you.. you would have 5x + 3 = 150
OK. just a minute.
Yes, I remember doing this.
OK.. Here is how you do it. going to be hard to write but here goes. (sin x + 1) / (cos x + (cos x/sin x)) = tan x { I substituted cos x / sinx for cot x OK so far?
I understand that part
Step 2 ... only look at the denominator and get a common denominator so cos x + (cos x/sin x) would have a common denominator od sinx x.. so I need to multiply cos x by (sin x / sin x) to get that common denominator. You would have (cos x sin x)/sinx + (cos x/sinx) on the bottom which turns into (cos x sin x) + cos x ALL OVER sin x OK?
sorry common denominator of sin x
ok, I got that too
OK. almost done When we take a fraction divided by a fraction we multiply by the reciprocal.. so we have (sin x + 1) divided by (cos x sin x + cos x)/sin x So we would multiply by the reciprocal to give us sin x + 1 times sin x /(cos x sin x + cos x) OK?
ok
Now you have to factor the denominator cos x sin x + cos x we factor that by taking out a common factor ex. 3x + 3 would factor into 3(x + 1) so this would be cos x(sin x + 1) OK?
ok
So then you would have (sin x + 1) * sin x/(cos x(sin x + 1)) If you write this as a fraction you will see that (sin x + 1) cancels out You are then left with sin x / cos x Which we know that sin x/cos x = tan x SO tan x = tan x
yes, thank you very much for showing the steps, it helps greatly, i started it but got stuck in the middle, thank you very much!
You are welcome

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