Question

cotA/1-cotA + tanA/1-tanA = -1
​

Answer 1

LHS : Cot A / 1-cot A + tan A / 1-tan A

or, Cos A / Sin A Sin A / Cos A

__________. + ___________

1-CosA/SinA 1 - Sin A / Cos A

Cos / (Sin A - Cos A ) + Sin A / (Cos A - Sin A )

or Cos^2 A - Cos A Sin A + Sin^2 A - Sin A Cos A

___________________________________

SinA Cos A - Sin^2 A - Cos^2 A - Sin A

or, 1-2 CosA SinA. [Sin^2 A + Cos^2 A = 1]

___________

-(SinACosA + Sin^2 A + Cos^2 A + SinA CosA)

or, (1-2CosASinA)

___________

-(1-2CosASinA)

or, 1/-1

or, -1 = RHS.