Question

The expression sinx(cscx - cotx cosx) can be simplified to.

Answer 1

do you know your trig IDs?

Answer 2

sin^2 x

sin^2 x - csc x

cos^2 x

sin x - tan x

Answer 3

what's csc(x) equals to?

Answer 4

csc is 1/sin x right?

Answer 5

i think

Answer 6

ahemm dunno

Answer 7

ok, let's use that for now

Answer 8

what about cot(x)?

Answer 9

1/tan?

Answer 10

well, yes and tan(x) is equals to?

Answer 11

sin/cos??

Answer 12

yes, thus cot(x) its inverse or cos/sin, thus, lemme type a few :)

Answer 13

?

Answer 14

$$
csc(x) = \cfrac{1}{sin(x)}\\
cot(x) = \cfrac{cos(x)}{sin(x)}\\
sin(x)\pmatrix{csc(x)-cot(x)cos(x)} \implies
sin(x) \pmatrix{\cfrac{1}{sin(x)}-\cfrac{cos(x)}{sin(x)}\times cos(x)}\\
sin(x) \pmatrix{\cfrac{1}{sin(x)}-\cfrac{cos^2(x)}{sin(x)}}\\
sin(x) \pmatrix{\cfrac{1-cos^2}{sin(x)}}\\
$$

Answer 15

can you recognize the identity that looks like \(\large 1-cos^2(x)\)?

Answer 16

/

Answer 17

do you happen to have your trig identities sheet?

Answer 18

does it show that \(sin^2+cos^2=1?\)

Answer 19

my teacher never gave me one

Answer 20

so the teacher just handed you out trig exercises without any formula sheets? tsk tsk tsk

Answer 21

we were suppose to memorize them in class but i keep forgetting them

Answer 22

http://i324.photobucket.com/albums/k326/hi_im_johji/Identities.jpg

Answer 23

that one has the one I just mentioned anyhow :/

Answer 24

ok
thx

Answer 25

if you don't have one, you'll need one

Answer 26

okay

Answer 27

so from \(sin^2+cos^2 =1\) , solve for \(sin^2\), what would that give you?

Answer 28

1-cos^2?

Answer 29

so sin^2 = 1-cos^2, thus
$$
csc(x) = \cfrac{1}{sin(x)}\\
cot(x) = \cfrac{cos(x)}{sin(x)}\\
sin(x)\pmatrix{csc(x)-cot(x)cos(x)} \implies
sin(x) \pmatrix{\cfrac{1}{sin(x)}-\cfrac{cos(x)}{sin(x)}\times cos(x)}\\
sin(x) \pmatrix{\cfrac{1}{sin(x)}-\cfrac{cos^2(x)}{sin(x)}}\\
sin(x) \pmatrix{\cfrac{1-cos^2}{sin(x)}} \color{green}{\implies
sin(x) \pmatrix{\cfrac{sin^2(x)}{sin(x)}} \implies sin(x)\pmatrix{\cfrac{sin(x)}{1}}}\\
$$

Answer 30

so, what would you get from that?

Answer 31

idk

Answer 32

so, what would say

a * (a/1)

give you?

Answer 33

a^2

Answer 34

well, say

2 * (2/1)

what would that give?

Answer 35

4

Answer 36

4 or \(2^2\)

so

a * (a/1)

would be?

Answer 37

a^2?

Answer 38

same * same = same^2

but I thought that'd be known by now :/

anyhow, any number over 1 is just itself

so, what would you get from the sin(x) expression?

Answer 39

sin^2x

Answer 40

so, that's the simplified version \(\large sin^2(x)\)

Answer 41

THXX! Sorry! I HATE TRIG!