Question

@Callisto

Answer 1

Hey @callisto! I have some trig Id problems

Answer 2

Yes?!

Answer 3

I already did a.

Answer 4

When we answer this type of question, Normally we try to prove both LHS and RHS right?

Answer 5

Or is it ok just do do one?

Answer 6

you can start with either LHS or RHS, say LHS, then you need to make it the same as the other side, that is RHS

Answer 7

Can you see the pic? O rshould I post a clearer one?

Answer 8

It's okay :)
Do you mind stating clearly what your question is?

Answer 9

Ohh, the question is Prove the following identities

Answer 10

Okay, that b as an example, can we?

Answer 11

Yes

Answer 12

LHS = (sinx +cosx)^2
= sin^2 x + 2sinxcosx + cos^2 x
= sin^2 x+ cos^2 x + 2sinxcosx
= 1 + 2sinxcosx
= RHS

So you just need to do one side and get the same thing as the other side... Would it be clearer to you?

Answer 13

@Open2study

Answer 14

Hey:)

Answer 15

Do you understand the proof above?

Answer 16

Ok, problem b, I think I get it now.
we will get sin^2 x + 2sinxcosx + cos^2 x
and when we add sin² x + cos² x, we get 1st pythagorean (If im not wrong)

Answer 17

that means that
sin² x + cos² x = 1

Answer 18

therefore, we will get 1 + (2sinx * cosx)

Answer 19

LHS = RHS

Answer 20

yes :)

Answer 21

ok, that made sense:)

Answer 22

Okay, can you try c?
You can start with the easier side. In this case, I think the RHS is easier :)

Answer 23

ok. I will try.

Answer 24

One question, If cotx = 1/tanx. in my problem, do i convert it to 1/(sinx/cosx)

Answer 25

Hmm.. you need the get the same thing as the other side. So that the others can know it is identical easily.
If LHS = 1/tanx , then you need to make RHS looks like the LHS, that is 1/tanx ,do you understand?

Answer 26

Yes, I get that part

Answer 27

Glad to hear that :)

Answer 28

Ok is the beginning to this kind of right?

RHS = cosx/sinx * 2sinx cosx

Answer 29

Yup!

Answer 30

Im stuck here:(. I have no idea how to make it identical to LHS

Answer 31

Sorry, gimme some time!!

Answer 32

How come cos 2x =1+ cos 2x? where does the 1 appear from?
Also,
LHS is 1+cos(2x) not 1+cos2x². there shouldnt be the ²

Answer 33

Sorry, my bad :(
cos 2x = 2cos^2x -1

In the 3rd step, we've got 2cos^2 x , that is equal to cos2x +1

Answer 34

wait so once we get 2cos²x, the next step will equal to 1+cos2x?

Answer 35

yes... do you understand how it comes?

Answer 36

No:(, Im a bit confused here

Answer 37

we know that cos2x = 2cos^2 x -1 , right?

Answer 38

yes

Answer 39

both sides add 1, what would you get?

Answer 40

We would get RHS, but why would we ad 1 to both sides?

Answer 41

cos2x = 2cos^2 x -1
cos2x +1 = 2cos^2 x

To change the subject, so that you can get 2cos^2 x =cos2x +1
and then you can get the answer :P

Answer 42

Ohh. okok. Thank you.

Answer 43

To solve problem d, do we use the 2nd pythagorean identity?

Answer 44

Hmm.. not sure, we don't call pythagorean identities here...

Answer 45

Cause if Im not wrong, a version of the 2nd pythagorean identity is tan² x = sec²x-1 right?

Answer 46

Or am I going the wrong path?

Answer 47

Sorry, one minute