# Prove that LHS=RHS

Another method:

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

On dividing numerator and denominator by sinA, we get,

= (cotA-1+cosecA)/(cotA+1-cosecA)

Now, using identity cosec^2 A – cot^2 A = 1, we get,

= [cotA+cosecA-(cosec^2 A – cot^2 A)]/[cotA-cosecA+1]

= [cotA+cosecA-(cosecA-cotA)(cosecA+cota)]/[cotA-cosecA+1]

= [cotA+cosecA (1-(cosecA-cotA))]/[cotA-cosecA+1]

= [(cotA+cosecA)(1-cosecA+cotA)]/[cotA-cosecA+1]

= [(cotA+cosecA)(cotA-cosecA+1)]/[cotA-cosecA+1]

= (cotA+cosecA)

= RHS