Prove that #(cosA - sinA + 1)/(cosA + sinA - 1) = cscA + cotA# ?

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Answer 1 · 2016-09-14T10:10:18

#LHS=(cosA-sinA+1)/(cosA+sinA-1)#

#=(sinA(cosA-sinA+1))/(sinA(cosA+sinA-1))#

#=(sinAcosA-sin^2A+sinA)/(sinA(cosA+sinA-1))#

#=(sinAcosA+sinA-(1-cos^2A))/(sinA(cosA+sinA-1))#

#=(sinA(cosA+1)-(1-cosA)(1+cosA))/(sinA(cosA+sinA-1))#

#=((1+cosA)(sinA+cosA-1))/(sinA(cosA+sinA-1))#

#=((1+cosA)cancel((sinA+cosA-1)))/(sinAcancel((cosA+sinA-1)))#

#=1/sinA+cosA/sinA#

#=cscA+cotA=RHS#

Proved