Question

IF 3SINX + 4COSX = 5 ; 4COSX - 3SINX = ?

Answer 1

(3sinx+4cosx)=5

(3sinx+4cosx)²=25

9sin²x+16cos²x+24sinx.cosx=25

9(1-cos²x)+16(1-sin²x)+24sinx.cosx=25

9-9cos²x+16-16sin²x+24sinx.cosx=25

-9cos²x-16sin²x+24sinx.cosx+25=25

9cos²x+16sin²x-24sinx.cosx=0

(3cosx)²+(4sinx)²-2(3cosx)(4sinx)=0

(3cosx-4sinx)²=0