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C3 Trig help needed

Question:IMG_20130715_135720-1.jpg. 9b

I'm stuck on that ^ question 9b and need help. I just did a LOT of random stuff and here's my very long working out in order:
IMG_20130715_140005.jpg
IMG_20130715_140132.jpg
IMG_20130715_140254-1.jpg

Sorry for the very long messy working out. Surprisingly the final identity there is right, but it is not what the question demanded :frown: . If you plug in x=30° into it and into 1+2tan^2 x , you end up with the same answer of 5/3. But I don't understand where I went wrong? Can someone please explain to me how I should approach the problem?

Thanks so much! :biggrin:
(edited 10 years ago)
Original post by krisshP
...


Going back to the start, with the LHS, you have the difference to two squares.

....

And don't forget an identity involving sec and tan.

Edit:

With your actual working, if you use sec2x=1+tan2x\sec^2x=1+\tan^2x at the end you'll get the desired result.
(edited 10 years ago)
Reply 2
Original post by ghostwalker
Going back to the start, with the LHS, you have the difference to two squares.

....

And don't forget an identity involving sec and tan.

Edit:

With your actual working, if you use sec2x=1+tan2x\sec^2x=1+\tan^2x at the end you'll get the desired result.


I used sec2x=1+tan2x\sec^2x=1+\tan^2x this identity for the first time ever as I'm new to it and just learnt it. The identity worked like a charm :smile: both at the start in the LHS and later on in my working, thanks! :smile: :biggrin:
(edited 10 years ago)

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