trignometry

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

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1. 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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