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TRIG HW HELP...identities?
Please help me verify(prove) this identity:
(tanx)(1+cos2x) = sin2x
By the way, those are not squared.
THANK YOU :)
2 Answers
- Tùng PhươngLv 49 years agoFavorite Answer
(tanx)(1+cos2x) = sin2x
----------------------------------
(tanx).[1+ cos(2x)] = sin(2x)
LS = (tanx).[(1 + cos(2x)]
= (tanx).[1 + cosx)^2 - (sinx)^2 ] -------------- cos(2x) = (cosx)^2 - (sinx)^2
= (tanx).[1 - (sinx)^2 + (cosx)^2 ] ------------ (sinx)^2 + (cosx)^2 = 1
= (tanx).[ (cosx)^2 + (cosx)^2 ] ---------------- or (cosx)^2 = 1 - (sinx)^2
= (sinx/cosx).(2).(cosx)^2
= (2).(sinx).(cosx) ---------------------------------- sin(2x) = 2.sinx.cosx
= sin(2x)
= RS (proved!)
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Hope this helps!
- 9 years ago
cos2x=(cosx)^2-(sinx)^2=2(cosx)^2 -1=1-2(sinx)^2
Use from this: cos2x=2(cosx)^2-1
Then remember the formula for sin2x
sin2x=2sinxcosx
and the definition of tanx.
That's it!
As a side note, trigonometry is easy once you solve a lot of exercises. It's easier to remember the formulas when you practise them to check identities. And at some point it turns to be a lot of fun!
