Question

Help me with verifying :)

Answer 1

\[1-(\frac{ 1-\cos^2x }{ 1+cosx }) = cosx\]

Answer 2

first, let's look at some familiar faces, shall we?
do you recognize 1-cos^2(x) from anywhere?

Answer 3

yess

Answer 4

identities :) let me look at my notes

Answer 5

sin^2

Answer 6

1-(sin^2x/1+cosx) = COSX

Answer 7

um, i think we should look at this identity;
cos^2 x + sin^2 x = 1
subtract sin^2 x from both sides to see something neat

Answer 8

cosx can turn inso 1/secx??

Answer 9

Jacky are we trying to do this like a proof?
Only making adjustments to one side of the equation?

Answer 10

yes^

Answer 11

cos^2x = 1-sin^2x?

Answer 12

ahhhhhhh

Answer 13

Hmm here is my approach.
Start by getting a common denominator,\[\Large\rm \frac{1+\cos x}{1+\cos x}-\frac{1-\cos^2x}{1+\cos x}\]

Answer 14

Combining the fractions gives us,\[\Large\rm \frac{1+\cos x-1+\cos^2x}{1+\cos x}\]

Answer 15

alrght common denominators...

Answer 16

but zepdrix i'm helping him and we can't both help him at once omg you're stealing my thunder D:

Answer 17

Oh soz :c
I'll simmer down

Answer 18

i like zep's method more :(

Answer 19

With these types of problems there are many different approachs,
was just trying to mix it up a lil bit hehe

Answer 20

alrighty, then go ahead zep. apparently he doesn't like me :"C

Answer 21

lol nooo

Answer 22

aw t.t the betrayal

Answer 23

Sooo from the last step I posted c:
The 1's cancel out yes?

Answer 24

\[\Large\rm \frac{\cos x+\cos^2x}{1+\cos x}\]

Answer 25

Any confusion as to why the `cos^2x turned positive when we combined the fractions`?

Answer 26

same denominator, so they both add to each other (the numerator)

Answer 27

My approach: \[
1-\cos^2(x) = (1-\cos(x))(1+\cos(x))
\]

Answer 28

denominator cancels.

Answer 29

Make sure you understand this little tidbit,
here is something they skip over in teaching math sometimes.\[\Large\rm -\frac{a+b}{c}=-\left(\frac{a+b}{c}\right)\]You can think of brackets existing around the fraction.
You have to distribute the negative to each term in the numerator.

Answer 30

Yah that's a better way to do it if you can remember the difference of squares!! :)
Saves you a few steps.

Answer 31

whoops

Answer 32

how do u write in big letters? with the formulas

Answer 33

With the equation tool, just below the text box.

Answer 34

the neagtive multiplied with the negative inside ... gotcha

Answer 35

You mean how to increase the text size?

Answer 36

yes

Answer 37

^thanks wio

Answer 38

\[\large\text{\large}\quad \Large\text{\Large}\quad \huge\text{\huge}\quad \Huge\text{\Huge}\]Use one of those words at the start of your equation.
You have to manually type it in.

Answer 39

okay now that we have (cosx+cos^2x) / 1+cosx

Answer 40

Hmmmm each term in the numerator has a cosine +_+
Maybe we can factor it out.

Answer 41

cos(1+cos)/ cancels with deno

Answer 42

hehe cosx=cosx

Answer 43

gracias amigo

Answer 44

yay good job \c:/

Answer 45

\*_*/

Answer 46

i have another one :o

Answer 47

\[\HUGE \frac{ cosx }{ 1-sinx } = \frac{ 1+sinx }{ cosx }\]

Answer 48

do i flip the sinx to a 1/cscx

Answer 49

Oh ummm....
No no keep sines and cosines.

Answer 50

Let's work with the left side,
Multiply top and bottom by 1+sinx

Answer 51

cross multiply is what i was missing

Answer 52

or not, just expanding

Answer 53

Cross multiplying kind of defeats the purpose of `manipulating one side` :(

Answer 54

\[\Large\rm \frac{\cos x}{1-\sin x}=\frac{\cos x(1+\sin x)}{(1-\sin x)(1+\sin x)}=\frac{\cos x(1+\sin x)}{1-\sin^2x}\]

Answer 55

ok 1+sinx(1-sinx) is an identity

Answer 56

how do u write in Equation mode so fast. it takes me forever

Answer 57

ah yes it is :3 i spilled the beans lol

Answer 58

I've been using it for a few months now D: got really comfortable doing basic stuff with it.

Answer 59

1-sin^2x is cos2x

Answer 60

cosx cancels

Answer 61

yay

Answer 62

do you remember all these identities and formulas or do you need a refenrece?

Answer 63

Ummmm I remember all of the basic ones.
I use them a lot in my classes still anyway.

I don't have ALL of the silly identities memorized though.
Like I couldn't tell you off the top of my head what the tangent double angle formula is.

Answer 64

Trig is really really deep though,
don't let it bother you if you haven't been able to memorize them all :\

Make sure you memorize your `square identities` though.
Those are really important.

Answer 65

\[\HUGE \tan(2\theta)=\frac{ 2\tan \theta }{ 1-\tan^2\theta }\]

Answer 66

:D why is it nit huge wtffff

Answer 67

It's case senstive,
\huge or \Huge
not \HUGE

Answer 68

hmm ok lets try it

Answer 69

hey abyssal

Answer 70

\[\Huge Cos^2\frac{ \alpha }{ 2 } = \frac{ \sin \alpha + \tan \alpha }{ 2\tan \alpha }\]

Answer 71

XD

Answer 72

Again though, these special functions are all case sensitive.
Don't type Cos
type cos instead

Answer 73

i think i got this one

Answer 74

let me

Answer 75

k

Answer 76

ah my game starting :CC I gotta go...
URF time!

Answer 77

league?

Answer 78

add me bruh