Question

csc theta *cot theta
-----------------
sec theta

Answer 1

\[\frac{ \csc(\theta)\cot(\theta) }{ \sec(\theta) }\]

Answer 2

Simplify this?

Answer 3

I assume so...
The answer choices are:
sec2θ

cot2θ

csc2θ

1

I worked it out but i came with a crazy answer

Answer 4

let me see

Answer 5

ok the answer is there... but its tricky. The best thing i do for these first is to change everything into sines and cosines. As you practice you'll see that a sec(theta) is a cosine(theta) on the other side of the denominator, and cosecant is a sine on the other side of the denominator. Does that make sense?

Answer 6

I am just really confused with these basic identities

Answer 7

cot square theta

Answer 8

Ok so how would i write that out? How would i get that answer?

Answer 9

working on it just a sec

Answer 10

i will explain

Answer 11

ok thank you

Answer 12

cosec theta=1/sin theta
cot theta = cos theta /sin theta
sec thete =1/cos theta

Answer 13

we get (cos theta/sin sqr. theta)(1/cos theta)

Answer 14

that is,(cos theta/sin sqr. theta)*(cos theta)

Answer 15

so cos sqr theta/sin sqr theta=(cos theta/sin theta)^2

Answer 16

got it?

Answer 17

Oh ok i understand, so i just plug in the alternate values for each and simplify it from there?

Answer 18

yes

Answer 19

are those squares above in your multiple choice answers?

Answer 20

you got to have hold on these values

Answer 21

See that makes alot more sense then the way they say it in my textbook

Answer 22

@druminjosh yes they must be sqrs

Answer 23

I have a table of equivalencies here... oh and yeah they are squares sorry about that

Answer 24

if you know those basic formulas you can change every identity

Answer 25

so do you see that

\[\frac{ \csc(\theta)\cot(\theta) }{ \sec(\theta) }=\frac{ \cos(\theta)\cot(\theta) }{ \sin(\theta) }\]

Answer 26

So how would i apply that to the squares... do i just double them?

Answer 27

Oh and @druminjosh i do thank you

Answer 28

ok what is cos / sin?

Answer 29

hmm??

Answer 30

@druminjosh would it be csc/sec

Answer 31

cos(theta)/sin(theta) = cot(theta) so you have cot(theta) * cot(theta)

Answer 32

so cot^2

Answer 33

yep yep :)

Answer 34

what about this problem... how would i set up the squares

Answer 35

what is cos^2+sin^2?

Answer 36

cot(theta)^2?

Answer 37

no cos^2+sin^2 is 1

Answer 38

I can explain why if you want.

Answer 39

This is really confusing... yes can you please?

Answer 40

This comes from pythagorean theorem and right triangle trigonometry. You know that a^2+b^2=c^2 yes?

Answer 41

Yes

Answer 42

ok i'm gonna dry to draw this but it might not look pretty

Answer 43

oh is it because csc and sec are opposites and therefore you are left with one?