Find the angle x if sin2x + 2sinx - cosx - 1 = 0.

To find x if sin2x+2sinx-cosx-1 =
0

We know that sin2x = sin(x+x) =
2sinxcosx.

Therefore substituting sin2x = 2sinxcosx in the
given equation, sin2x+2sinx -cosx -1 = 0, we get:

2sinxcosx
+2sinx -cosx -1 = 0.

2sinx (cosx+1) - 1(cosx+1) =
0.

(cosx-1)(2sinx-1) =
0.

Equating each factor to zero we
get:

cosx-1 = 0 . Or 2sinx -1=
0

cosx -1 = 0 gives cosx = 1. So x = 2npi, n =
0,1,2,...

2sinx -1 = 0 gives sinx = 1/2 . Or  x = npi +
(-1)^n*pi/6, n = 0, 1,2,....