Trigonometry Help..!?

Question

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

Answer 1

cosx / ( 1 - sinx )

Multiply denominator and numerator with 1 + cosx + sinx

 

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

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

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

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

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