Question

prove that cosx+sinx/cosx-sinx=tan(pai/4+x)​

Answer 1

RHS=tan(pai/4+x)=(tanpi + tanx)/(1-tanpi tanx)

=(tan45+tanx)/(1-tan45tanx)

=(1+tanx)/(1-tanx) since tan45=1

=(1+sinx/cosx)/(1-sinx/cosx)

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

=cosx+sinx/cosx-sinx

=LHS