Question

verify the identity and show all work 1- tanxtany= cos(x+y)/cosxcosy

Answer 1

Do I have to work each side independently?

Answer 2

We know that cos(x + y) = cosxcosy - sinxsiny @cicichenxx, right?

Answer 3

YEAH I THINK SO

Answer 4

I DONT KNOW HOW TO DO WITH THE LEFT SIDE

Answer 5

cosxcosy - sinxsiny / cosxcosy
= cosxcosy/cosxcosy - sinxsiny/cosxcosy
= 1 - tanxtany

Answer 6

should i do something with the left side or do nothing?

Answer 7

hello?

Answer 8

is somebody here?

Answer 9

I was disconnected from the q, sorry.

Answer 10

i really appreciated your help, but i still confused with the 1-tanxtany

Answer 11

What you do is basically focus on the right side, don't worry about the left side, the right side will be equal to it........
cos(x+y)/cosx cosy
(cos x cos y - sin x siny ) / (cos x cos y)
cos x cos y/cos x cos y - sin x sin y / cos x cos y
1-tanx tany

See?

Answer 12

yeah i got it thanks and there is another question can you help me with that?

Answer 13

I suck at math, but I can try.

Answer 14

cot(x+y)=(cotxcoty-1)/(cotx+coty)

Answer 15

it's ok just try it

Answer 16

Looking at the left side
\[\cot(x+y) \]
cos(x+y) / sin(x+y)
[(cosxcosy - sinxsiny) / (sinxcosy + cosxsiny)]
Divide numerator and denominator by sinxsiny, we get
(cotxcoty-1)/(coty+cotx),

Answer 17

yes i got it. and there are two questions i need to do（secx+cscx)/(tanx+cotx)=sinx+cosx cosx/(1-sinx)=secx+tanx

Answer 18

do you have time?

Answer 19

Yes, but can you please make a new question?

Answer 20

@cicichenxx, tag me if you want to, just like I tagged you!

Answer 21

how to tag you

Answer 22

（secx+cscx)/(tanx+cotx)=sinx+cosx

Answer 23

@SolomonZelman, @cicichenxx

Answer 24

cosx/(1-sinx)=secx+tanx @SolomonZelman

Answer 25

Yup, you just tagged me!

Answer 26

（secx+cscx)/(tanx+cotx)=sinx+cosx @SolomonZelman

Answer 27

do you get them?

Answer 28

i an waiting for your answer

Answer 29

Looking at the left side,

sec(x)+csc(x)/tan(x)+cot(x)
(1/cos(x) + 1/sin(x)) / (sin(x)/cos(x) + cos(x)/sin(x))
((sin(x) + cos(x)) / sin(x)cos(x)) / ((sin^2(x) + cos^2(x)) / sin(x)cos(x)
sin(x) + cos(x) / 1
sin(x) + cos(x)

Answer 30

Good?

Answer 31

yeah i am thing about it

Answer 32

so these questions just do one side is ok?

Answer 33

Yes, you make one side equal to the other.
That's the definition of these questions, work one of the sides independently.

Answer 34

cosx/(1-sinx)=secx+tanx @SolomonZelman

Answer 35

perhaps this is the lat one i really confusing about those equations

Answer 36

@SolomonZelman are you here?

Answer 37

i really confusing about those equations @SolomonZelman

Answer 38

1) cos(x) / (1-sin(x))
Multiply top and bottom by (1 + sin(x)). This gives you
[cos(x)(1 + sin(x))] / (1 - sin^2(x)) =
[cos(x)(1 + sin(x))] / cos^2(x) =
(1 + sin(x)) / cos(x) =
sec(x) + tan(x)
or
Secx + tanx = cosx / (1-sinx)
Taking Left side, = Secx + Tanx
sec x = 1/cos x and
tan x = sin x / cox x
Putting the values of secx and tanx you will get
= secx + tanx
= 1/cosx + sinx / cosx
By Taking LCM you will get
= (1 + sinx) / cosx
Multiply the numerator and denominator by (1-sinx)
= (1-sinx)(1+sinx) / cosx(1-sinx)
= (1-sin^2 x) / (cos x - sin x cos x)
As 1-sin^2 x = cos^2 x therefore;
= cos^2 x / [cosx (1-sin x)]
Divided numerator and denominator by (cosx) you will get
= cosx / (1-sin x)

Answer 39

i need to think about this, thank for your patient

Answer 40

Anytime!

Answer 41

If you just don;t get it, I can reword it.

Answer 42

Solve 0.4 cos(x) = sin(2x). SolomonZelman

The smallest positive solution is_______

The next smallest positive solution is_____

Answer 43

Solve 0.4 cos(x) = sin(2x). @SolomonZelman

The smallest positive solution is_______

The next smallest positive solution is_____