案例介绍christine教程.pptx

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案例介绍christine教程.pptx

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11:ProvingTrigIdentities?ChristineCrisp“TeachALevelMaths”

Vol.2:A2CoreModules

Certainimagesand/orphotosonthispresentationarethecopyrightedpropertyofJupiterImagesandarebeingusedwithpermissionunderlicense.Theseimagesand/orphotosmaynotbecopiedordownloadedwithoutpermissionfromJupiterImagesModuleC3AQAEdexcelOCRModuleC4MEI/OCR

Also,Anyofthetrigidentitieswe’vemetsofar,canbeusedtoproveotheridentities.So,weneedtobefamiliarwiththedefinitions:andthe3quadratictrigidentities:

e.g.1ProvethatThemethodistostartwiththel.h.s.anduseanyidentitiestoconvertitstepbystepintother.h.s.Thereisoftenmorethanonewayofdoingit.Ifwegetstuckworkingfromthel.h.s.,wecanstartwithther.h.s.Theidentitysymbol...Wemustalwaysquotetheidentitiesused.Wekeeplookingatther.h.s.toseewherewewanttogetto.shouldbeusedbutoftenisn’t.

e.g.ProvethatNowIchangetothereciprocal:Finally,InoticethatIhaveasquareofandwantasquareof:Ther.h.s.isareciprocalcontainingasquaresoIwanttouseanidentityforthel.h.s.thatinvolvessquaresandleadstoareciprocal.Wealwaysstartlikethis.Proof:l.h.s.

ProvethatAnotherwayoftacklingthesameproblemisasfollows:(Commondenom.)Proof:l.h.s.

ExerciseProvethefollowingidentities:2.1.3.

Proof:l.h.s.1.ProveSolutions:

2.Prove(Nobracketswanted)(Cancel)Proof:l.h.s.InoticedthatIwantbutnot

3.(Usedtwice)(Collectterms)(Splitfractionaswewant2terms)1Proof:l.h.s.

Thefollowingslidescontainrepeatsofinformationonearlierslides,shownwithoutcolour,sothattheycanbeprintedandphotocopied.Formostpurposestheslidescanbeprintedas“Handouts”withupto6slidespersheet.

Also,Anyofthetrigidentitieswe’vemetsofar,c