Trig identity qstn (1 Viewer)

[Speed6]

Prove:


ty

 

[leehuan]

Use sec^2(x) = 1 + tan^2(x) and cosec^2(x) = cot^2(x) + 1

You find LHS = RHS = 1


(Or what VBN commented below. I would've seen that they both equal to 1 on the spot as well, however I assume in an exam they may want you to show working out so...)

 

[VBN2470]

. Done

 

[InteGrand]

Prove:


ty

 

[Speed6]

hmm it was simple but it stumped me,

thanks everyone!

 

[Speed6]

Ok so the next question isn't really a question which I need help for, but I would like to see if there is a different approach you would take to this question, I have already proved it but I would like someone else to prove it just so I can see how you do it

 

[Shadowdude]

Ok so the next question isn't really a question which I need help for, but I would like to see if there is a different approach you would take to this question, I have already proved it but I would like someone else to prove it just so I can see how you do it

don't you just convert all the cot, cosecs and secs to normal tan, sin and cos and then go about it normally?

 

[Speed6]

don't you just convert all the cot, cosecs and secs to normal tan, sin and cos and then go about it normally?

Yes, but to what extent do you mean by 'normally'?

 

[Speed6]

I can put up my soln if you want, then you can see what could of been done,if anything else could be done...

 

[Shadowdude]

the reason i don't like these types of question is that all you need really is to know what cosec, sec and cot mean and it's... trivial

Like if you expand and simplify, it resolves down to sin = sin, which is obviously true


But then you have to keep in mind when expressions are undefined and everything, and then sorta go backwards.


The way I like doing these questions is showing that the original problem is equivalent to something else, which is equivalent to something else (and this is that process of seeing what it's equal to and converting cosecs, secs and cots), and then reducing it to something like sin = sin, which is true. Then you go to the next question.

Which isn't really a "proof" of anything, it's just... yeah.

 

[Speed6]

the reason i don't like these types of question is that all you need really is to know what cosec, sec and cot mean and it's... trivial

Like if you expand and simplify, it resolves down to sin = sin, which is obviously true


But then you have to keep in mind when expressions are undefined and everything, and then sorta go backwards.


The way I like doing these questions is showing that the original problem is equivalent to something else, which is equivalent to something else (and this is that process of seeing what it's equal to and converting cosecs, secs and cots), and then reducing it to something like sin = sin, which is true. Then you go to the next question.

Which isn't really a "proof" of anything, it's just... yeah.

Exactly right.

Well I like these types of questions which in order to satisfy you must manipulate bs.

Yes, I see what you mean and going to back to one of the first points which you have made, they (identities) are always/usually trivial in nature.

 

[Shadowdude]

I like the LHS = RHS ones which involve the more complex trig. identities like 1 + tan^2 = sec^2 or some variant where it's not as simple as "oh okay, well cot is cos/sin and csc is 1/sin and sec is 1/cos, plug that in, simplify, oh look i get 2 = 2 or something"

At least try and trip up the student

 

[Speed6]

I like the LHS = RHS ones which involve the more complex trig. identities like 1 + tan^2 = sec^2 or some variant where it's not as simple as "oh okay, well cot is cos/sin and csc is 1/sin and sec is 1/cos, plug that in, simplify, oh look i get 2 = 2 or something"

At least try and trip up the student

I love challenging questions hue