Question #9586d

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Answer 1 · 2016-11-10T15:17:31

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

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

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

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

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

$=(cosxcancel((cosx- sinx)))/cancel((cosx-sinx))$

$=cosx=RHS$

Proved