Question

if a and b are two values of x lying between 0 and 360 which satisfy equation 6cosx+ 8sinx=9 then what will be the value of sin(a+b)

Answer 1

I got this from another forum. Not my own solution.
6cosx+8sinx=9
6cosx-9=-8sinx
3(2cosx-3)=-8sinx
Squaring both sides
9(4cos^2x+9-12cosx)=64sin^2x
Substitute cosx = p and also sin^2x = 1-cos^2x. Hence sin^2x = 1-p^2
9(4p^2+9-12p)=64(1-p^2)
36p^2+81-108p=64-64p^2
100p^2-108p+17=0
simplify and u will get 2 valus of p
substitiue in a and b