1 (Edexcel, Further Pure Math, 2013 jan, Paper 2, No 2)
Using the identities sin(A+B)=sinAcosB+cosAsinBcos(A+B)=cosAcosB–sinAsinBtanA=sinAcosA
(a) show that tan(A+B)=tanA+tanB1−tanAtanB (3)
(b) Hence show that
(i) tan105∘=1+√31−√3
(ii) tan15∘=√3−11+√3 (4)
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