Question

prove that sinA+1-cosA/(cosA-1+sinA) =1+ sinA/cosA​

Answer 1

Answer:

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

L.H.S.

=[sinA+(1-cosA)]/[sinA-(1-cosA)]

Multiplying by [sinA+(1-cosA)] in Nr and Dr.

=[sinA+(1-cosA)]^2/[sin^2A-(1-cosA)^2]

=[sin^2A+2.sinA.(1-cosA)+(1-cosA)^2]/[(1-cos^2A)-(1-cosA)^2]

=[(1-cos^2A)+2.sinA.(1-cosA) +(1-cosA)^2]/[(1-cosA)(1+cosA) - (1-cosA)^2].

=(1-cosA)[1+cosA+2sinA+1-cosA]/(1-cosA)[1+cosA-1+cosA].

=[2+2sinA]/[2.cosA].

=2(1+sinA)/2.cosA.

= (1+sinA)/cosA , proved.