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Using double identity, show… = tan²x

It seems that to be trig identities is definitely my weakest link in maths. I keep doubting myself

Show 1-cos 2x ÷ 1+ cos 2x=tan ² x

The only way that I can link cos with tan is to use the tan x=Sin x÷ Cos x

I think I have the right idea but my result is negative 2tan²x

See attached:

Upon writing this, I believe I have failed to expand the bracket correctly, so it would be 1-1+2sin²x÷ 1+ 2cos²x.

I can’t use cos 2x=cos ²x-sin²x as this would be tan ²x=0

(edited 1 year ago)

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Reply 1

RDKGames

Study Forum Helper

Original post by KingRich

There's double angles on the LHS but a single angle on the RHS. This instructs you to use the double angle identities and simplify from there.

If you have done this and are getting -tan^2 then that just means you're making a sign error somewhere. Maybe you're not substituting in the correct signs when applying double angle identities.

EDIT: looking at your attachment, you didn't expand the numerator correctly. Also, don't lay out your work like this when writing the answer in the exam. It's better to lay it out as:

(LHS) = .... = .... = .... = (RHS)

whereas you are laying it out as

(LHS) = (RHS)
.... = (RHS)
.... = (RHS)
.... = (RHS)
(RHS) = (RHS)

(edited 1 year ago)

Reply 2

KingRich

Original post by RDKGames

Okay. I see what you mean.

mmm, you mean the part when I’ve drawn an arrow. I had corrected this in my original comment.

But upon inspection, I believe I am correct. As 2 would cancel out and hence leave tan²x

Reply 3

Skiwi

Original post by KingRich

Okay. I see what you mean.

mmm, you mean the part when I’ve drawn an arrow. I had corrected this in my original comment.

But upon inspection, I believe I am correct. As 2 would cancel out and hence leave tan²x

Be careful with the brackets, -(1-2sin^2x) is -1+2sin^2x

Reply 4

KingRich

Original post by Skiwi

Be careful with the brackets, -(1-2sin^2x) is -1+2sin^2x

Yes, I had already confirmed my error in the first comment I had posted.

But thank you for confirming

Reply 5

Muttley79

Original post by KingRich

You MUST NOT put the expressions equal to each other - that is a huge error.

You need to cinnsider the LHS and RHS separately.

Reply 6

KingRich

Original post by Muttley79

You MUST NOT put the expressions equal to each other - that is a huge error.

You need to cinnsider the LHS and RHS separately.

to confirm, is this layout correct?

Or.

(edited 1 year ago)

Reply 7

the bear

here is how you can set out a typical trig proof:

keep the left side separate from the right side.

work on both sides until you get a match

Reply 8

Muttley79

Original post by KingRich

to confirm, is this layout correct?

No - split the two sides.

LHS triple equals .... [is equivalent to, not just equals]

and show you get the RHS

or vice versa.

Hasn't your teacher explained this?

Reply 9

KingRich

Original post by Muttley79

No - split the two sides.

LHS triple equals .... [is equivalent to, not just equals]

and show you get the RHS

or vice versa.

Hasn't your teacher explained this?

I don’t have a teacher. I’m home studying the whole a level myself, which is why I ask a lot of questions on here for support

Reply 10

KingRich

Original post by the bear

here is how you can set out a typical trig proof:

keep the left side separate from the right side.

work on both sides until you get a match

So, you’re saying I should draw a line down the middle to show them as separate? I thought it looked clear there’s a LHS and RHS

Reply 11

the bear

Original post by KingRich

So, you’re saying I should draw a line down the middle to show them as separate? I thought it looked clear there’s a LHS and RHS

i am not saying anything. you can do what you like.

Reply 12

KingRich

Original post by the bear

i am not saying anything. you can do what you like.

Well, suggesting. Lol

Reply 13

KingRich

Original post by Muttley79

No - split the two sides.

LHS triple equals .... [is equivalent to, not just equals]

and show you get the RHS

or vice versa.

Hasn't your teacher explained this?

As bear suggested.

would I have to something like this when dealing with identities? Clearly labelled

E33FE221-395D-4693-AEB5-209FC29EF44B.jpeg182.2KB

Reply 14

Muttley79

Original post by KingRich

As bear suggested.

would I have to something like this when dealing with identities? Clearly labelled

Don't write tan^2 at the top at all write LHS triple equals etc

You just work on one side not both.

State which rule you are using to move from one line to the next

Finish when you get the RHS exactly.

Reply 15

Skiwi

Original post by KingRich

Yes, I had already confirmed my error in the first comment I had posted.

But thank you for confirming

Didn't see the response, apologies

Reply 16

KingRich

Original post by Muttley79

Mmm, okay. I’ll take the advice and put it to work and please let me know next time if I’m still making the error. Thanks

Reply 17

mqb2766

Without wanting to prolong this,
https://www.tuitionmath.com/single-post/2016/12/09/11-tips-to-conquer-trigonometry-proving
has a few decent tips about how to go about common trig identity questions (and how to spot them) as well as a reasonable way to write them up. Pretty much as hinted at as above, and there should be similar examples in your textbook.

(edited 1 year ago)

Reply 18

KingRich

Original post by mqb2766

Lol, I think I just acknowledged my error.

I believe this to make better sense

Or,

Thanks for the link

(edited 1 year ago)

Reply 19

mqb2766

Original post by KingRich

Lol, I think I just acknowledged my error.

I believe this to make better sense

Thats certainly an improvement. A few minor things,
* Dont overuse brackets (as in the previous posts). tan^2(x) is much better than (tan^2 x)
* Put a small amount of explanation in when youre using a double angle identity or whatever. Should the marker read down the left column first, then start at the top of the right column or .... of your answer?
* If you start at the LHS of the desired identity, say something like that at the start.