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

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Answer 1 · 2016-04-17T00:20:05

See below

LHS =left hand side, RHS =right hand side

LHS $=(cosx/(1+sinx)) xx (1-sinx)/(1-sinx) - 2/cosx$

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

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

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

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

$=(-1-sinx)/cosx$

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

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

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

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

$=cosx/(sinx-1)$

$=RHS$

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