amaths question

sec2x = (2﹣cosx﹣sinx)/(1﹣sinx)

1 + tan2x = (1﹣cosx)/(1﹣sinx) + 1

tan2x = (1﹣cosx)/(1﹣sinx)

(1﹣sinx)(tan2x) = (1﹣cosx)

sin2x﹣sin3x = cos2x﹣cos3x

sin2x﹣cos2x = sin3x﹣cos3x

(sinx+cosx)(sinx﹣cos x) = (sinx﹣cosx)(sin2x + sinxcosx + cos2x)

sinx﹣cosx = 0 or sinx+cosx = 1 + sinxcosx

tanx = 1 or 1+sinxcosx﹣-sinx﹣cosx = 0

tanx = 1 or 1﹣sinx+cosx(sinx﹣1) = 0

tanx=1 or (1﹣cosx)(1﹣sinx)= 0

tanx=1 or sinx = 1 or cosx = 1

x=0o,45o,90o,225o,360o

sec90o is undefined,so x is not 90o

∴x = 0o, 45o, 225o,360o