another question (1 Viewer)

[Gruma]

yet another question from the diagnostic test in the cambridge book, i wish theyd put worked solutions in the back like the lee book; nehow.....


Q14) use De Moivre's theorem with n = 2 to show that
cos 2 = cos^2 - sin^2 and sin 2 = 2 sin cos.
hence show that tan 2 = 2 tan / 1 - tan^2


this question has me stumped, probably coz i cant remember my trig rules. i can show that cos 2 = cos^2 - sin^2 and
sin 2 = 2 sin cos but i cant seem to show the tan part.

comon guys i need your help my tests 2morro.

 

[Gruma]

oh yeah that stupid thing is spose to be a theta, if thats how u spell it.

 

[spice girl]

Originally posted by Gruma
yet another question from the diagnostic test in the cambridge book, i wish theyd put worked solutions in the back like the lee book; nehow.....


Q14) use De Moivre's theorem with n = 2 to show that
cos 2 = cos^2 - sin^2 and sin 2 = 2 sin cos.
hence show that tan 2 = 2 tan / 1 - tan^2


this question has me stumped, probably coz i cant remember my trig rules. i can show that cos 2 = cos^2 - sin^2 and
sin 2 = 2 sin cos but i cant seem to show the tan part.

comon guys i need your help my tests 2morro.

tan 2 = sin 2 /cos 2
= 2 sin cos / (cos^2 - sin^2)
=2(sin/ cos)/(1 - (sin^2/cos^2 ) ..................divide by cos^2
= 2 tan / 1 - tan^2 as required

 

[Gruma]

answer thanks

Thanks for the help Spice Girl I'm crammin for the test tomorro

 

[spice girl]

Re: answer thanks

Originally posted by Gruma
Thanks for the help Spice Girl I'm crammin for the test tomorro

hehe good luck

 

[Twintip]

We weren't tested on De Moivre's theorem in our half-yearlies. Is it in the syllabus? Can't seem to find it anywhere (although we have learnt it).

 

[McLake]

Originally posted by Twintip
We weren't tested on De Moivre's theorem in our half-yearlies. Is it in the syllabus? Can't seem to find it anywhere (although we have learnt it).

Yes, its in the syllabus:

SECTION 2.4 - Powers and Roots:
Students are able to:
- Prove, by induction
(cos@ + isin@)ⁿ = cosn@ + isinn@ (for all integer n)
- Find any integer power of a given complex number
- Find the complex nth roots of +/- 1 in mod-arg form