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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