If `max{5sin theta+3sin(theta-alpha)}=7` then the set of possible vaues of `alpha` is `theta in R`

Explanation

`5 sin theta + 3 sin( theta - alpha)`

`= ( 5 + 3 cos alpha) sin theta - 3sin alpha cos theta`

`= {(5 + 3cos alpha)^2 + 9 sin^2 alpha}`

`= sqrt((5+ 3 cos alpha)^2 + 9 sin^2 alpha) sin(theta - phi) `

`max{5sin theta + 3 cos(theta- alpha)} `

`= sqrt((5+3cos alpha)^2 + 9sin^2alpha)`

=`7`

`25 + 30 cos alp-ha + 9 = 49`

...