Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Prove: rot 1+sina / 1- sina = (sina/2 + cosa/2) / (sina/2 - cosa/2)?

1. cosec? + 2cosec 2? / sec? = cot?/2

2. 1+tanatan2a = sec2a

3. 2sin? sin2?/ cos? + cos3? = tan2?tan?

4. sin3?/sin? - cos3?/cos? = 2

5. cos3?/cos? + sin3?/sin? = 4cos2?

6. (tan?/2 + cot ?/2) / (cot?/2 - tan?/2)

7. sin3?/cos? + cos3?/ sin? = 2cot2?

I was working on my assignment questions and I got stuck in those.. can you please help me !!

Thank you

The format of these is all the same -- you just need to apply identities. My advice is to convert everything into sines and cosines, and work from the more complicated-looking side to the more simple-looking side. I'm not going to give you the solutions to these problems, but good tricks to look out for are:

(i) Getting rid of

2\theta

s by using double-angle identities (unless they appear on both sides, in which case leave them there)
(ii) Getting rid of

3\theta

s by writing

3\theta = 2\theta + \theta

and using the angle-addition formulae
(iii) Doing (i) and (ii) in reverse (e.g. writing

\sin \theta \cos \theta

in terms of

\sin 2\theta

)
(iv) Looking out for things in the form

\sin^2 A + \cos^2 A

OP

I do try doing these methods but it just doesn't work for me !;(

Original post by Abady.f

I do try doing these methods but it just doesn't work for me !;(

Well show your working! No-one here's going to do 7 questions for you.

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