Tuesday, 30 August 2016

algebra precalculus - Find cos(2alpha) given cos(thetaalpha) and sin(theta+alpha)

My question is:




If cos(θα)=35 and sin(θ+α)=1213, find cos(2α).




Attempt I:
cos2(θα)+sin2(θ+α)=925+144169cos2(θα)cos2(θ+α)=925+1441691=8964225.


But I thought it won't work.



Then I tried this:



Attempt II:
{cosθcosα+sinθsinα=cos(θα)=35,sinθcosα+cosθsinα=sin(θ+α)=1213,cosθ(sinα+cosα)+sinθ(sinα+cosα)=9965,2[sin(α+π4)cos(απ4)]=9965.


But I thought here its better to convert both parts to cosines, so I did:
2[cos(απ4)cos(απ4)]=9965,2cos2(απ4)=9965.

But I think it also didn't work ....



Please guide. Thanks.

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