prove that a)sinx-cosx+1/sinx+cosx-1=secx+tanxb)if 2cosx+sinx=1,then find the value of 7cosx+6sinxc)find the values of xand y for which cosecA=x2-y2/x2+y2is satisfied

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 = sec x + tan x

Dear Student,
Please find below the solution to your problem.

a) 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
= sec x + tan x

(b)
(c)


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