Find the value of sinx ,if 8sinx-cosx=4

Answer 1

8sinx-cosx = 4
8sinx = cosx+4
64sin^2x = cos^2x + 8cosx + 16
64-64cos^2x = cos^2x + 8cosx + 16
65cos^2x + 8cosx - 48 = 0
(5cosx-4)(13cosx+12) = 0
cosx = 4/5 or -12/13
so, sinx = 3/5 or 5/13