trignometry

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if alpha and beta are 2 different values of θ lying between 0 and 2π which satisfy the equation 6cosθ+8 sinθ=9 find the value of sin alpha + beta.i want the answer by quadratic method. can u help solving sum by that method

  • trignometry -

    Oh well, if you do not like WLS' cool method then

    cos T = sqrt(1 - sin^2 T)

    6 sqrt(1 -sin^2 T) + 8 sin T = 9
    let sin T = x

    6 sqrt(1-x^2) + 8 x = 9

    6 sqrt (1-x^2) = 9-8x

    36 (1-x^2) = 81 - 144x + 64 x^2
    36 -36 x^2 = 81 - 144x + 64 x^2
    100 x^2 -144 x + 45 = 0
    x = [ 144 +/- sqrt (20736 - 18000)]/200
    x = [ 144 +/- 52.3 ]/200
    x = .981 or .4585
    but x is sin T so
    T = 78.8 or T = 27.3
    sum = 106.1
    sin(106.1) = .961

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