Question #49ba0

1 Answer
Jan 23, 2017

To prove

sinx (1+tanx) + cosx (1+cotx) = (sinx + cosx) / (sinxcosx

LHS=sinx (1+tanx) + cosx (1+cotx)

=sinx/cosx (cosx+cosx*tanx)+ cosx/sinx (sinx+sinx*cotx)

=sinx/cosx (cosx+cosx*sinx/cosx)+ cosx/sinx (sinx+sinx*cosx/sinx)

=sinx/cosx (cosx+sinx)+ cosx/sinx (sinx+cosx)

=(sinx+cosx)(sinx/cosx + cosx/sinx )

=(sinx+cosx)((sin^2x+ cos^2x)/(sinxcosx ))

=(sinx+cosx)/(sinxcosx )=RHS

Proved