trigonometry!!!!!!!!!!!!!!!!!!!!!!

Question

prove that

 

(1-cos 2x)/(2sinx + sin 2x) = tax (x/2)

Answer 1

LHS = (1 - cos2x) / (2sinx + sin2x)

         = (1 - (1 - 2sin^2x) / (2sinx + 2sinxcosx)  [ Since cos2x = 1 - 2sin^2x and sin2x = 2sinxcosx ]

         = (1 - 1 + 2sin^2x) / (2sinx(1 + cosx))

         = 2sin^2x / (2sinx(1 + cosx))

         = sinx / (1 + cosx)

         = tan(x/2)                                               [ Since sinx / (1 + cosx) = tan(x/2) half angle formula ]

         = RHS

Hence it is proved that (1 - cos2x) / (2sinx + sin2x) = tan(x/2)