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 #