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Core 4 - Trig double angle question

prove the given identity

2cos⁡θ32\cos \theta^3 + sin⁡2θ\sin 2\theta sin⁡θ\sin \theta= 2cos⁡θ2\cos \theta

and the double angle formula for sin is 2sinxcosx (or feta in this case)
and when i try to get 2cosfeta it goes horribly wrong
anyone have any ideas i could do?
thanks x
Reply 1
Avatar for Zoob1
Zoob1
2cos^3A + sin2AsinA =
2cos^3A + 2sin^2AcosA =
2cos^3A + 2(1 - cos^2A)(cosA) =
2cos^3A + 2(cosA - cos^3A) =
2cos^3A + 2cosA - 2cos^3A =
2cosA

Sorry if it's hard to read i dont know how to use that maths thing. :smile:
very good question!!!!
hot angel 02
prove the given identity

2cos⁡θ32\cos \theta^3 + sin⁡2θ\sin 2\theta sin⁡θ\sin \theta= 2cos⁡θ2\cos \theta

and the double angle formula for sin is 2sinxcosx (or feta in this case)
and when i try to get 2cosfeta it goes horribly wrong
anyone have any ideas i could do?
thanks x


Just to clarify what Zoob1 said:
Considering the LHS:
⇒2cos⁡3θ+2sin⁡2θcos⁡θ\Rightarrow 2 \cos ^3 \theta + 2\sin^2\theta \cos\theta
⇒2cos⁡3θ+2(1−cos⁡2θ)cos⁡θ\Rightarrow 2\cos^3\theta + 2(1-\cos^2\theta)\cos\theta
⇒2cos⁡3θ−2cos⁡3θ+2cos⁡θ\Rightarrow 2\cos^3\theta - 2\cos^3\theta + 2\cos\theta
⇒2cos⁡θ\Rightarrow 2\cos\theta QED.
Reply 4
Avatar for hot angel 02
hot angel 02
OP
Im on a next set of questions, still using the double angels and triple angels
im asking to integrate sin²3x
the answer is 1/2x - 1/12sin6x
i just have no idea which formula to use :s-smilie:
can anyone help?
Use the identity for cos 2x (the one involving sin^2 x)
Reply 6
Avatar for hot angel 02
hot angel 02
OP
When you think your doing well, you get stuck AGAIN! lol
so this time im asked to integrate cos^3 x dx
i got the answer to be 1/3sin3x + sinx but the book has got sinx + 1/3 sin^3 x
can anyone help?
Reply 7
Avatar for rnd
rnd
6
cos^3(x)=cos(x)cos^2(x)

Now use cos^2(x)=1-sin^2(x)
hot angel 02
prove the given identity

2cos⁡θ32\cos \theta^3 + sin⁡2θ\sin 2\theta sin⁡θ\sin \theta= 2cos⁡θ2\cos \theta

and the double angle formula for sin is 2sinxcosx (or feta in this case)
and when i try to get 2cosfeta it goes horribly wrong
anyone have any ideas i could do?
thanks x


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