Question

2sin a+3 cos a =2 then 3 sin a -2 cos a =

Answer 1

(2 Sin a + 3 Cos a =2)*3
let (3 Sin a -2 Cos a =x)*2
6 sin a + 9 cos a=6.......(1)
6 sin a -4 cos a =2x.....(2)
(1)-(2):

13 cos a=6-2x
cos a= (6-2x)/13
cos²a=(6-2x)²/13².......(3)

6 sin a - 4 (6-2x)/13=2x
6sina=2x + (24-8x)/13
6sina = (26x+24-8x)/13
sin a= (18x+24)/78
sin a=(3x+4)/13
sin²a= (3x+4)²/13²......(4)

add (3) and (4)
1=[(6-2x)²+(3x+4)²]/13²
169=36+4x²-24x+9x²+16+24x
169-52=13 x²
117=13x²
x²=9
x=±3