Friday, 9 June 2017

algebra precalculus - If fracasinA=fracbcosA, show that sinAcosA=fracaba2+b2




I don't know how to go about solving this, I think I need to use sin2θ+cos2θ=1, but I'm not sure how to go about this.



The closest I managed to get was:



asinA=bcosA
acosAbsinA=0
a2cos2A+b2sin2A2abcosAsinA=0
cosAsinA=a2cos2A+b2sin2A2ab




Which seems to vaguely resemble what I need, but I'm not sure of the final steps.


Answer



Notice that
sinAcosA=sinAcosAsin2A+cos2A=tanAtan2A+1
It should be ease for you to continue.


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