If `alpha, beta` are two different values of x lying between `0 and 2pi` which satisfy the equation `6 cos x + 8 sin x = 9`, find the value of `sin (alpha + beta)`

Explanation

Given,

`6 cos x + 8 sin x = 9 ... (i)`

=`8sinx=9−6cosx`

=`(8sinx)^2=(9−6cosx)^2`


=`64sin^2x=81+36cos^2x−108cosx`

=`64(1−cos^2x)=81+36cos^2x−108cosx`

=`64−64cos^2x+64cos^2x−108cosx+81−64=0`

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