Question

verify each identity

Answer 1

@ganeshie8

Answer 2

@satellite73

Answer 3

Post which identity you want to do.

Answer 4

HI!!

Answer 5

not that easy to read sideways is it? let me turn my head and see if i can figure one out

Answer 6

sorry it's number 16 @Directrix

Answer 7

\[\csc \theta+\cot \theta= \frac{ \sin \theta }{ 1-\cos \theta }\]

Answer 8

oh ok mostly this usually algebra
lets see how far we get doing that

Answer 9

is it fine to work with the left side?

Answer 10

which side is that for?

Answer 11

that is the left side, i put \(\cos(x)=a, \sin(x)=b\)

Answer 12

alas it is a mistake, dang

Answer 13

\[\frac{1}{b}+\frac{a}{b}=\frac{1+a}{b}\]

Answer 14

is that like an equation to use or did you make that up to assit the problem?

Answer 15

so the left side is \[\frac{1+\cos(x)}{\sin(x)}\] and the right is
\[\frac{\sin(x)}{1-\cos(x)}\] now these are equal, but we have to show it some how

Answer 16

it is easier to see with letters rather than sine and cosine
makes the algebra easier
also makes writing it easier
most of it is algebra

Answer 17

now if you want to turn
\[\frac{1+\cos(x)}{\sin(x)}\] in to
\[\frac{\sin(x)}{1-\cos(x)}\] you can do it by multiplying top and bottom by \(1+\cos(x)\)

Answer 18

dang another typo
multiply by \(1-\cos(x)\)

Answer 19

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

Answer 20

i'm a little confused so we're working with the right side

Answer 21

?

Answer 22

no turned the left in to the right

Answer 23

you want me to try and write it in one line?

Answer 24

csc=1/sin

Answer 25

i'm trying to take it step by step, tell me if i'm getting info wrong. so frist you looked at csc right?

Answer 26

which is 1/sin?

Answer 27

then you looked at cot which is cos/sin?

Answer 28

right

Answer 29

then added them up

Answer 30

which is easy because the denominators are the same

Answer 31

Exactly, then you multipled it by (1-cos)

Answer 32

right , top and bottom

Answer 33

\[(1^2-2(1)(\cos \theta)+\cos \theta^2)/\sin \theta- \cos \theta \sin \theta\]

Answer 34

dont multiply out in the bottom
leave in factored form

Answer 35

also \((1+a)(1-a)=1-a^2\)

Answer 36

so your numerator is wrong

Answer 37

what would the denominator be?

Answer 38

\[\sin(x)(1-\cos(x))\]

Answer 39

dont multiply out, leave it in factored form so you can cancel

Answer 40

cancel what?

Answer 41

i got the answer

Answer 42

ok good