Question

sinxtanx/1-cosx=secx+1

Answer 1

sinxsinx/cos-cossquarex =sin2x/cosx-cos2x

Answer 2

LHS
= (1-cosx) (1+secx)

secx = 1/cosx

LHS = (1-cosx)(1+1/cosx)
= 1 + 1/cosx - cosx - cosx*1/cosx
= 1/cosx - cosx
= (1-cos^2x)/cosx

now we know that
sin^2x + cos^2x = 1
so sin^2x = 1 - cos^2x

so we get
LHS = sin^2x/cosx
= sinx / cosx * sinx
= sinx * tanx
= RHS
Hence proved