Question

is cos²x/2 = 1+cosx/2 AND cosx/2 = ±√1+cosx/2 Same thing??

Answer 1

If you mean

\[\Large \cos^2\left(\frac{x}{2}\right) = 1+\cos\left(\frac{x}{2}\right)\]

is the same as

\[\Large \cos\left(\frac{x}{2}\right) = \pm\sqrt{1+\cos\left(\frac{x}{2}\right)}\]

then you are correct

Answer 2

OKay thank you so much!

Answer 3

np

Answer 4

is it possible for you to check my work?

Answer 5

sure

Answer 6

so it said to verify the identity of 2cscx cos²(x/2)= sinx/1-cosx

Answer 7

i will write down the steps i know so far

Answer 8

ok

Answer 9

somy first step i did was this!

Answer 10

but i dont know what is next....could you please help me

Answer 11

From there, multiply top and bottom of (1+cos)/(sin) by (1-cos)

Tell me what you get

Answer 12

okay i am almost done please wait for a moment!

Answer 13

ok

Answer 14

you nailed it, very nice work

Answer 15

I'm sure you already know this, but it's important to keep in mind. When dealing with identities, you only manipulate one side. So you convert one side to the other.

Answer 16

okay! thank you so much!!

Answer 17

you're welcome

Answer 18

Sorry to ask you again but How do you verify the identities of cos²(x/2) = secx+1 / 2secx ??? i got steps done if you could check

Answer 19

How do you verify the identities of cos²(x/2) = secx+1 / 2secx ???

Answer 20

sec = 1/cos

Answer 21

so cos*sec = cos*(1/cos) = cos/cos = 1

Answer 22

this means

(1+cos)*sec = sec + 1

Answer 23

sorry i am really lost

Answer 24

do you see how sec = 1/cos

Answer 25

yes i get that part

Answer 26

do you see how

cos*sec = cos*(1/cos) = cos/cos = 1

?

Answer 27

but before we started the this question dont you multiply the conjugate? so wouldnt it be 1+cosx (1-cosx) and 2(1-cosx )???

Answer 28

you could do that (it's perfectly valid), but you'll be getting further away from what we want (which has a sec in it)

Answer 29

They multiplied by sec/sec because they wanted to introduce a 'sec' term

Answer 30

ok...could you explain a bit in detail about the sec term? I am so sorrrrry :((

Answer 31

we have (1+cos)/2

Answer 32

yes

Answer 33

we want a sec term in the denominator (along with the 2), so we multiply 2 by sec

Answer 34

but we must do the same to the numerator to keep things balanced (and equivalent)

Answer 35

okay

Answer 36

so do you see how/why they got the answer?

Answer 37

hmm,,? like this ?

Answer 38

close, distribute that "sec" through to every term in the numerator

Answer 39

I'm sure you know this (by now), but when I say "sec" I mean "sec(x)", but I find it easier to type "sec"

Answer 40

okay im kind of lost