Posted by usha on Saturday, June 11, 2011 at 6:54am.
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

trig  drwls, Saturday, June 11, 2011 at 7:55am
0.6 cosè + 0.8 sinè = 0.9
Let sinx = 0.6; then
cosx = 0.8 and x = 36.87 degrees
sinx cosè + cosx sinè = 0.9
sin (x + è) = 0.9
x + è = 64.16 degrees or 115.84 degrees
alpha = è1 = 27.29 degrees
beta = è2 = 78.97
alpha + beta = 106.26 degrees
sin (alpha + beta) = 0.9600

trig  Reiny, Saturday, June 11, 2011 at 8:16am
drwls,
that is amazingly clever.

trig  usha, Saturday, June 11, 2011 at 10:21am
thank you very much. can u solve the same by quadratic equation method

trig  drwls, Saturday, June 11, 2011 at 11:24am
yes, it can be done that way, but I'd rather leave that to you.
Write it as
6cosθ= 9  8 sinθ
Square both sides and the left side can be written 36(1  sin^2 θ)
Then you have a quadratic in sin theta to solve. Have fun.
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