Question

Help please will medal!

Simplify (tan^2 theta + 1)/(tan^2 theta)

Answer 1

explain how you solved it too!

Answer 2

hmm you have \(\frac{\tan^2\theta+1}{\tan^2x}\)
remember that 1+tan^2x=sec^2x

Answer 3

so you have sec^2x/tan^2x following

Answer 4

The answer is apparently csc^2 theta but I don't know how to get to that

Answer 5

@xapproachesinfinity

Answer 6

asked are you following what i did!
did you understand it

Answer 7

not really...

Answer 8

eh sorry i used x instead of theta

Answer 9

ok

Answer 10

i said that tan^2x+1=sec^2x this an identity you should know

Answer 11

ok

Answer 12

so the top becomes
sec^2x
so we got sec^2x/tan^2x

Answer 13

good so far

Answer 14

yep

Answer 15

ok,
now that tanx in sin and cosine

Answer 16

what is*

Answer 17

we know that tanx=sinx/cosx correct

Answer 18

correct

Answer 19

ok
so it follow that tan^2x=sin^2x/cos^2x

Answer 20

ok

Answer 21

now we got sec^2x/(sin^2x/cos^2x)

Answer 22

ok

Answer 23

i just replaced tan^2x by what's in the bottom

Answer 24

ok

Answer 25

now you flip the fraction in the bottom
to get sec^2x (cos^2x/sin^2x)

Answer 26

that makes sense

Answer 27

to go from division to multiplication you flip the fraction right

Answer 28

ok good

Answer 29

right

Answer 30

now what is sec^2x

Answer 31

it should be 1/cos^2x since secx=1/cosx

Answer 32

right?

Answer 33

right

Answer 34

okay
now we got
(1/cos^2x)*(cos^2x/sin^2x)=1/sin^2x after canceling cos^2x

Answer 35

what!

Answer 36

you got the cancellation part?

Answer 37

yeah

Answer 38

we have \(\huge \frac{1}{cos^2x}\frac{cos^2x}{sin^2x}\)

Answer 39

correct

Answer 40

if we cancell we get \(\huge \frac{1}{sin^2x}\)
and what it that?

Answer 41

any chance you know what that might be?

Answer 42

csc^2x?

Answer 43

yeah! we have sinx=1/cscx so it follows that sin^2x=1/csc^2x

Answer 44

Thank you so much for the help!!

Answer 45

that means also csc^2x=1/sin^2x it is the same thing

Answer 46

welcome!