Question

A?

Answer 1

so here's why it's not A

Answer 2

or

Answer 3

cos^2(x) + sin^2(x) = 1 so...

Answer 4

1/cosx = secx so A is actually True

Answer 5

alright, any thoughts on B?

as a hint cos^2(x) + sin^2(x) = 1 as we stated before

Answer 6

So D/

Answer 7

good, D is the false one

Answer 8

A

Answer 9

hm

well you can split cot into cos/sin giving us:

sin(x) + cos(x) * cos(x) / sin(x)

any ideas what you can do from there?

Answer 10

Oh B

Answer 11

nope not quite

Answer 12

Actually I do not want toguess. No, I am not sure what to do from here

Answer 13

we can re-write sin(x) as sin^2(x)/sin(x) to get

sin^2(x)/sin(x) + cos^2(x)/sin(x)

now, since sin^2(x) + cos^2(x) equals 1 what do you think the final result might be?

Answer 14

D

Answer 15

nopr its c

Answer 16

sin^2(x)/sin(x) + cos^2(x)/sin(x) = 1/sin(x) = csc(x)

Answer 17

I apologize I'm not too well aware on these concepts

Answer 18

C

Answer 19

ok I finally figured it out

first you have to expand (csc(x) + cot(x))^2 using foil

it ends up being

csc^(x) + 2csc(x)cot(x) + cot^2(x)

now, we know that csc^(x) = 1 + cot^(x)

so if you substitute csc^(x) = 1 + cot^(x) into the equation csc^(x) + 2csc(x)cot(x) + cot^2(x)

what do you get?

Answer 20

Um D?

Answer 21

good

Answer 22

B

Answer 23

well it's kind of hard to do this one w/o giving it away, but if you start with the last identity and convert the cot and tan expressions to sin and cos you will see that you end up with sin^2(x) + cos^2(x) = 1 cross out like terms, making D the best possibility

Answer 24

true

Answer 25

yup good

Answer 26

B

Answer 27

weeel this one is also a little hard to do w/o giving it away but B is wrong b/c that's not a mathematically valid step, C is a bit too far to be a first step

the reason we multiply the denominator and numerator by 1 + sin(x) in answer choice A is to convert the denominator to 1 - sin^2(x) which = cos^2(x)

Answer 28

so A is your best possibility

Answer 29

f?

Answer 30

good

Answer 31

C

Answer 32

good but there's one more, you may need to re-arrange the equations to see it clearly

Answer 33

A

Answer 34

that's close but keep in mind sin^2(x) + cos^2(x) = 1 is the identity not a minus sign

Answer 35

D

Answer 36

good so C+ D

Answer 37

A

Answer 38

A is actually not an identity

sec(x) = 1/cos
csc(x) = 1/sin

Answer 39

there are two correct choices, try looking at B C and D to see which one is false

Answer 40

B is right

Answer 41

good, keep going

Answer 42

and so is C

Answer 43

D*

Answer 44

hm

remember that sec(x) = 1/cos(x)

that means 1/sec(x) = cos not tan

so the correct sol'ns are B +D

Answer 45

True

Answer 46

I'm going to say false on this one, if you try plugging in various x-values you won't get (sqrt(3) + 1) / 2 every single time