Prove that sinx-cosx+1/sinx+cosx-1=1/secx-tanx

1.	Prove that sinx-cosx+1/sinx+cosx-1=1/secx-tanx
Answer» sinx-cosx+1/sinx+cosx -1=(sinx-cosx+1)x(sinx +cosx +1) / (sinx+cosx - 1)x(sinx +cosx +1)=(sinx +1)sq. - (cosx)sq./ (sinx +cosx) sq. - (1)sq.=sinsq.x+2sinx+1-cossq.x/ sinsq.x+cossq.x+2sinxcosx-1=2sinsq.x+2sinx/ 2sinxcosx=2sinx(sinx +1)/ 2sinxcosx=sinx+1/cosx=(1+sinx)x(1-sinx)/ (cosx) x(1-sinx)=cosx/(1-sinx) (dividing num. and den. by cosx) =1/secx-tanx PROVED BY SIDDHARTH THE

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