If 3 cot A = 4, check whether (1-tan^2 A)/(1+tan^2 A) = cos^2 A - sin^2 A or not

if  3cotA= 4 check whether
1-tan2A/1+tan2A =  cos2A – sin2A or not.
Ans:
 [note:You can solve it without using value]
RHS = cos2A – sin2A
[using  formula sin2A + cos2A = 1 hence cos2A =  1- sin2 ]
  ∴RHS = 1-sin2A – sin2A
            = 1- 2sin2A ………… (i)
LHS = 1-tan2A/1+tan2A
      = [1– sin2A/cos2A] /[1+ sin2A/cos2A]
      = [cos2A – sin2A/cos2A] /  
                                [cos2A+sin2A/cos2A ]
     = cos2A – sin2A/cos2A X
                                  cos2A /cos2A+sin2A
   = cos2A – sin2A / cos2A+sin2A
[using  formula sin2A + cos2A = 1]
  = 1-sin2A –sin2A / 1- sin2A +sin2A
  = 1- 2 sin2A / 1
 = 1- 2 sin2A  …………….. (ii)
From Eqn (i) & (ii) it is proved that
LHS = RHS proved and hence
1-tan2A/1+tan2A =  cos2A – sin2A