trignometry
posted by usha .
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

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(1x^2) + 8 x = 9
6 sqrt (1x^2) = 98x
36 (1x^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