Question

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?

Answer 1

Where is the = sign?

Answer 2

oh sorry i forgot... = tan
sin x + 1 / cos x + cot x = tan x

Answer 3

What did you do first?

Answer 4

The first step I did was change the cot in denominator into cos and sin

Answer 5

After I did that then I precedded with 1+ sin x/ (sin x)(cos x) + cos x/ sin

Answer 6

Tell me in the original problem. is sin x by itself and then 1/cosx by itself and then cotx by itself....

Answer 7

Ok, the original problem : (sin x +1) / (cos x + cot x) = tan x

Answer 8

Oh.. ok then just a minute.

Answer 9

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?

Answer 10

I don't follow... i thoght you multiply by the reciprocal..

Answer 11

i have to work on one side to equal the other side, which is tan x

Answer 12

(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.

Answer 13

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.

Answer 14

Yes, it is legal to do both sides, however my professor wants us to work it by choosing complex side to prove other side

Answer 15

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

Answer 16

OK. just a minute.

Answer 17

Yes, I remember doing this.

Answer 18

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?

Answer 19

I understand that part

Answer 20

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?

Answer 21

sorry common denominator of sin x

Answer 22

ok, I got that too

Answer 23

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?

Answer 24

ok

Answer 25

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?

Answer 26

ok

Answer 27

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

Answer 28

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!

Answer 29

You are welcome