Question

A & C ?

Answer 1

A and C are not equivalent so they can't both be the correct solution

A is true, now if we replace cos^2(x) with 1 - sin^(x) what do we get?

Answer 2

D

Answer 3

other way around

cos^2(x) - sin^2(x) becomes 1 - sin^2(x) - sin^2(x) which results in B not D

so A+B = your sol'n

Answer 4

3/10

Answer 5

hm

I got something a little different, I used the tan half angle identity:

Answer 6

sin(x) = 3/5 and cos(x) = -4/5

so tan(x/2) = (3/5)/(1 - 4/5) if I did this correctly

Answer 7

lemme just double check

Answer 8

2.5

Answer 9

check your calculations again

what is 3/5 divided by 1/5? as a hint you can cross out the denominators since they're equal

Answer 10

3

Answer 11

good so that's your sol'n

Answer 12

B and C

Answer 13

keep in mind, 2cos(x)cos(y) cannot be equal to both B and C, it has to be one or the other

Answer 14

B

Answer 15

alright, the proof is very complex but I'll try to break it down

cos(x+y) + cos(x-y) = 2cos(x)cos(y)

using the double angle identity

cos(x+y) = cos(x)cos(y) - sin(x)sin(y) [you just have to know this identity]

cos(x-y) = cos(x)cos(y) + sin(x)sin(y) [you just have to know this identity]

adding these together gives us

cos(x+y) + cos(x-y) = 2cos(x)cos(y) [since the sin expressions cancel out]

Answer 16

that's why there needs to be a plus sign in between the cos expressions not a minus sign

Answer 17

anyway, besides that, there's one more correct identity, do you know what it might be?

Answer 18

well, there's only two options left, A and D

let's look at tan(x-pi) = tan(x)

do you remember what the period of tan is?

Answer 19

A

Answer 20

good, since the period of tan is pi, then tan(x-pi) just shifts the graph over by pi units and ends up being equal to tan(x)

so A+C = your sol'n

Answer 21

D

Answer 22

well c too :/

Answer 23

keep in mind it's asking for the exact value; any decimal values are rounded not exact

Answer 24

so d

Answer 25

good

Answer 26

well done

Answer 27

D And A ?

Answer 28

yikes

this might take me a while to do the calculations ;-;

Answer 29

Its fine, like can you like really just sum it up or no? If not, then I will just submit A and D. Don't worry about it.

Answer 30

well I have a pretty good hunch that A is not one of the options, I can't think of an identity that would relate sin and tan like that

Answer 31

anyway, if you take

(cosx + sinx)^2 and expand this using foil what do you get?

Answer 32

1+2cos(x)sin(x)

Answer 33

awesome! and if you remember from before, 2cos(x)sin(x) = sin(2x)

so we get 1 + 2sin(x) making B true

Answer 34

anyway, if we look at C, we can use the identity

cos^2(x) - sin^2(x) = cos(2x)

if you replace "x" with "3x"

is C true or false?

Answer 35

true

Answer 36

good

any thoughts on D? it's a pretty tedious calculation so I wouldn't really blame you too much if you just plugged it into a calculator ;_;

Answer 37

False

Answer 38

good, so just B + C

the proof is here if you ever have a spare moment ;_; http://lazi.vn/uploads/edu/answer/1506788483_3.jpg

Answer 39

False

Answer 40

Sory I am going through this fast. I have a fever and need to get this done :(

Answer 41

good

Answer 42

T

Answer 43

have to be careful on this one, the identity is cos(x)sin(y) not cos(y) so this ends up being false

Answer 44

Yeah I just realized that:/

Answer 45

A

Answer 46

i get 2 for the denominator that is screwing me up

Answer 47

I get the answer that is in choice B but with a denominator of 2

Answer 48

SO B

Answer 49

using theta/2 = 17pi/8, you get theta = 17pi/4

therefore:

Answer 50

yeah, B, there's a plus sign not a minus sign due to the nature of the formula

Answer 51

I hope you feel better soon :S

Answer 52

Oh hey thanks ^^