Question

how do do you solve this step by step!!!?? click attached!! http://bamboodock.wacom.com/doodler/bfc956c3-fe7e-4954-8c89-656a6a83061f

Answer 1

i first converted sin^2 to 1-cos^2

Answer 2

well if you transpose some few things...
\[\cos x = 1 - \sin^2 (\frac x2)\]
\[\implies \cos x = \cos^2 (\frac x2)\]
is this what you did?

Answer 3

wait how did it become cos^2?

Answer 4

like you said \[\cos^2 = 1 - \sin ^2\]
then i just copied the "argument" of sin^

Answer 5

sin^2 *

Answer 6

\[\sin^2 x + \cos^2 x = 1\]
\[\sin ^2 (2x) + \cos^2 (2x) = 1\]
\[\sin^2 (3x) + \cos^2 (3x) = 1\]
\[\sin^2 (\frac x2) + \cos^2 (\frac x2) = 1\]
making sense now?

Answer 7

yes!!

Answer 8

so cosx = cos ^2 (x/2) what is the next step from here?

Answer 9

so now im thinking you do half-angle formula on that x/2

\[\cos x = [\cos (\frac x2)]^2\]
so what is the value of cos(x/2)?

Answer 10

im lost... half angle formula is this right?

Answer 11

yup

Answer 12

yes that is right

Answer 13

but its different from yours...why?

Answer 14

so this becomes \[\cos x = \left[\sqrt{\frac{1 + \cos x}{2}} \right]^2\]
what do you mean different from mine?

Answer 15

oh because cosx^2

Answer 16

yes.. (cos x)^2

Answer 17

wait... (cos x/2)^2

Answer 18

yes i made a mistake

Answer 19

so now... what is \[\left[\sqrt{\frac{1 + \cos x}{2}} \right]^2\]

Answer 20

im still lost ><

Answer 21

what are you lost about?

Answer 22

are you lost how i got that? or what to do next?

Answer 23

is it like this?

Answer 24

i dont know what to do next...><

Answer 25

yes it looks like that

Answer 26

do you remember this algebra rule: \[\huge (\sqrt a)^2 \implies a\]

Answer 27

yes

Answer 28

so then what would be \[\huge \left[\sqrt{\frac{1 + \cos x}{2}} \right] ^ 2\]

Answer 29

so it becomes liek this!?

Answer 30

definitely

Answer 31

do you have an idea what to do next now?

Answer 32

could you check my work!?

Answer 33

where?

Answer 34

can this happen?

Answer 35

sadly..no

Answer 36

here's a hint

when you have something like
\[\huge a = \frac{2+a}{4}\]
simply multiply both sides by 4
\[\huge \implies 4a = 2 + a\]
does that help?

Answer 37

so it becomes 2cosx = 1+ cosx

Answer 38

correct

Answer 39

now is the next step obvious to you?

Answer 40

cosx = cosx?

Answer 41

what did you do?

Answer 42

i really dont know the steps. like how do you remmber them>< im so lost

Answer 43

think of this as algebra

right now you have
\[2\cos x = 1 +\cos x\]
you can look at this like
\[2a = 1 + a\]
does that help?

Answer 44

oh a = 1 so cosx = 1?

Answer 45

RIGHT!

Answer 46

now...the final step is to solve for x

Answer 47

x = 0

Answer 48

correct!!

Answer 49

ahh thank you thank yoyu !!!!!

Answer 50

welcome welcome ^_^ just performing my avatar duties :DDD

Answer 51

your a champ!

Answer 52

you can check by substituting x = 0 in
\[\sin ^2 (\frac x2) + \cos x = 1\]
\[\implies \sin^2 (\frac 02) + \cos (0) = 1\]
\[\implies \sin^2 (0) + \cos (0) = 1\]
\[\implies 0 + 1 = 1\]
\[\implies 1 = 1 \checkmark\]