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Further Trigonometry Identity (Proving question)

  1. Jan 25, 2015 #1
    1) Question:
    Show that (sin3A-sinA)/(cosA+cos3A)=tanA

    2) Relevant equations:
    tan A=sinA/cos A
    1+tan^2A=sec^A
    cot A=1/tanA
    cot A=cos A/sinA
    sin^2A+cos^2A=1
    secA=1/cos A
    cosecA=1/sinA
    1+cosec^2A= cot^2A
    sin2A=2sinAcosA
    cos2A=1-2sin^2A=cos^2A-sin^2A=2cos^A-1
    tan2A=(2tanA)/1-tan^2A

    3)Attempt:
    (sin3A-sinA)/(cos A+cos3A)
    =(2sin3/2Acos3/2A)-(sinAcosA)/(cos^2(1/2)A-sin^2(1/2)A)+(cos^2(3/2)A-sin^2(3/2)A)
    I tried expanding but ended up confusing myself...
     
  2. jcsd
  3. Jan 25, 2015 #2
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