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March 29, 2017

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cos@-4SIN@=1 then sin@+4cos@=

  • trig - ,

    From the first:
    cosØ - 1 = 4sinØ
    square both sides
    cos^2 Ø - 2cosØ + 1 = 16sin^2 Ø
    cos^2 Ø - 2cosØ + 1 = 16(1 - cos^2 Ø)
    17cos^2 Ø - 2cosØ - 15 = 0
    (17cosØ + 15)(cosØ - 1)
    cosØ = -15/17 or cosØ = 1

    case1: cosØ = -15/17
    then sinØ = 8/17 (in 2nd quad)
    then sinØ + 4cosØ = 8/17 + 4(-15)/17 = -52/17

    or

    sinØ = -8/17 (in 3rd quad)
    then sinØ + 4cosØ = -8/17 + 4(-15/17) = -68/17

    Case 2: cosØ = 1
    then sinØ = 0
    and sinØ + 4cosØ = 0 + 4(1) = 4

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