very basic C3 help

Hi, I have just been doing an edexcel m2 'show that' question and I cannot reach the answer as I do not know some identities since I am an AS level student.

I would greatly appreciate it if somebody could list some basic identities. The one in the question I couldn't do was as following:

1/(cos^2theta)=sec^2theta

then sec^2theta=tan^2theta+1

I do not need understanding, I just would like a few identities that I can memorise for M2 on friday, since its a mechanics exam just the basic ones please.

One last thing, how does one solve costheta-sintheta? I squared it and found the answer to be 1-2sin(theta)*cos(theta), how do I go further.

Thanks

Reply 1

bartbarrow

cos^2+sin^2 = 1, from your AS.

You can find 2 more by dividing both sides by cos^2 and sin^2 to get
1 + tan^2 = sec^2
cot^2 + 1 = cosec^2

sec is 1/cos
cosec is 1/sin
cot is 1/tan

What do you mean "solve cosx-sinx"?

Reply 2

xyz9856

Original post by bartbarrow

Thank you for your response

I mean simplify it, I think I saw the simplified answer as something like sin2x? Just a bit of clarification

Reply 3

James Hp

Original post by xyz9856

Thank you for your response

I mean simplify it, I think I saw the simplified answer as something like sin2x? Just a bit of clarification

It's called a double angle identity - look it up.

sin(2x)= 2sin(x)cos(x)

There are some for each sin cos and tan.
Oh and if you go to the C3 page in the formula booklet, there are identities that you could use to derive them pretty easily by using the same angle - the one for sin (A + B) etc. (so you don't have to remember them)

Good luck

(edited 7 years ago)

Reply 4

HapaxOromenon3

Original post by xyz9856

Thank you for your response

I mean simplify it, I think I saw the simplified answer as something like sin2x? Just a bit of clarification

cos^2x - sin^2x is one of the possible expressions of cos(2x).
It can be rearranged as cos^2x - (1-cos^2x) = 2cos^2x - 1, which is the form of cos(2x) that you will probably be most familiar with.

Reply 5

bartbarrow

Original post by xyz9856

Thank you for your response

I mean simplify it, I think I saw the simplified answer as something like sin2x? Just a bit of clarification

If you've not heard of it and it's required for M2 (which exam board are you doing? I don't think it's part of AQA) then either your teacher has messed up considerably.

Reply 6

xyz9856

Original post by bartbarrow

If you've not heard of it and it's required for M2 (which exam board are you doing? I don't think it's part of AQA) then either your teacher has messed up considerably.

Edexcel

Anything with C3 trig very rarely comes up in M2, I looked through at least 10 papers to find a question I could not do due to it being part of C3. The only identity I can see being used is sec=1/cos and then 1+tan^2 really. I've already committed it to memory, as well as the double angle formulae for sin cos and tan. Im just being over-cautious because i'd like to get an A* on friday so its less stressful for me next year to get 270 UMS average.