There seems to be a flaw in your approach ....
-2sinx.cos3x = 0
then sinx = 0
cos 3x = 0
so,
sinx = 0
x= n
But note the difference here .......
cos 3x = 0
that 3x lies on the y axis ....
So 3x= (2n+1)
/2
or x = (2n+1)
/6
so finally solving like this we get x = n
or x = (2n+1)
/6
Now take the second approach ...
sin 2x(1- 2cos2x) = 0
then sin2x= 0
and cos 2x = 1/2
sin2x= 0
2x= n
or x = n
/2
cos 2x = 1/2
2x = 2n
+
/3 or 2x = 2n
-
/3
Thus this yields solution x = n
/2 , n
+
/6 or n
-
/6
Now one can easily establish a one to one correspondance between two solutions .. both soultions represent same set ...
cheers
![[Post New]](/templates/default/images/icon_minipost_new.gif){kind=icon}
![[Up]](/templates/default/images/icon_up.gif "[Up]"){kind=icon}
477
2
