Question #24406

1 Answer
P dilip_k
Feb 19, 2017

#LHS=(sina-cosa+1)/(sina+cosa-1)#

As in the numerator of RHS is #cosa#, we multiply #cosa# with both numerator and denominator of LHS and proceed to simplify it to get the expression of RHS.

So #LHS=(cosa(sina-cosa+1))/(cosa(sina+cosa-1))#

#=(cosa(sina-cosa+1))/(cosa*sina+cos^2a-cosa))#

#=(cosa(sina-cosa+1))/(cosa*sina+1-sin^2a-cosa)#

#=(cosa(sina-cosa+1))/((1-sina)(1+sina)-cosa+cosasina)#

#=(cosa(sina-cosa+1))/((1-sina)(1+sina)-cosa(1-sina))#

#=(cosa(cancel(sina-cosa+1)))/((1-sina)(cancel(sina-cosa+1)))#

#=cosa/(1-sina)=RHS#

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