Question #32e1a

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Answer 1 · 2017-02-13T01:57:39

#LHS=cosx/(1-tanx)+sinx/(1-cotx)#

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

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

#=cos^2x/(cosx-sinx)-sin^2x/(cosx-sinx)#

#=(cos^2x-sin^2x)/(cosx-sinx)#

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

#=sinx+cosx=RHS#

Proved