How do you verify $(1+sinx+cosx)/(1+sinx-cosx)=(1+cosx)/sinx$ ?

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Answer 1 · 2018-04-30T22:21:47

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

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

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

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

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

$=(1+cosx)/sinx=RHS$

How do you verify (1+sinx+cosx)/(1+sinx-cosx)=(1+cosx)/sinx(1+sinx+cosx)/(1+sinx-cosx)=(1+cosx)/sinx?