How do you prove cosx/(1+sinx)-2secx=cosx/(sinx-1)cosx1+sinx2secx=cosxsinx1?

1 Answer
Apr 17, 2016

See below

Explanation:

LHS =left hand side, RHS =right hand side

LHS=(cosx/(1+sinx)) xx (1-sinx)/(1-sinx) - 2/cosx=(cosx1+sinx)×1sinx1sinx2cosx

=(cosx (1-sinx))/(1-sin^2x) -2/cosx =cosx(1sinx)1sin2x2cosx

=(cosx(1-sinx))/cos^2x - 2/cos x=cosx(1sinx)cos2x2cosx

=(1-sinx)/cosx - 2/cos x=1sinxcosx2cosx

=(1-sinx-2)/cosx =1sinx2cosx

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

=-(1+sinx)/cosx xx (1-sinx)/(1-sinx)=1+sinxcosx×1sinx1sinx

=-(1-sin^2x)/(cosx(1-sinx))=1sin2xcosx(1sinx)

=-cos^2x/(cosx(1-sinx))=cos2xcosx(1sinx)

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

=cosx/(sinx-1)=cosxsinx1

=RHS =RHS