Question

prove that (sinx-cosx+1)/(sinx+cosx-1)=1/(secx-tanx) ​

Answer 1

Answer:

Step-by-step explanation:

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

Answer 2

Answer:

Step-by-step explanation:

inx-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