My question is:
If cos(θ−α)=35 and sin(θ+α)=1213, find cos(2α).
Attempt I:
cos2(θ−α)+sin2(θ+α)=925+144169⇒cos2(θ−α)−cos2(θ+α)=925+144169−1=8964225.
But I thought it won't work.
Then I tried this:
Attempt II:
{cosθcosα+sinθsinα=cos(θ−α)=35,sinθcosα+cosθsinα=sin(θ+α)=1213,cosθ(sinα+cosα)+sinθ(sinα+cosα)=9965,√2[sin(α+π4)cos(α−π4)]=9965.
But I thought here its better to convert both parts to cosines, so I did:
√2[cos(α−π4)cos(α−π4)]=9965,√2cos2(α−π4)=9965.
But I think it also didn't work ....
Please guide. Thanks.
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