Cot^2a(seca_1)/1+sina=sec^2a(1_sina /1+seca)

OK  I got it

if we divide the left side by the right side  and it simplifies to 1 then its proved

cot^2 A (sec A - 1)(1 + sec A)      cot^2 A (  sec^A - 1)
 =  
sec^2 A (  sinA + 1)(1 - sinA)       sec^2 A ( 1 - sin^2 A)

Now sec^2 A - 1 = tan^2 A and 1 - sin^2 A = cos ^2A so the fraction becomes

cot^2 A . tan^2 A

sec^2 A .  cos^2A  

Now cot^2 A = 1 / tan^2 A and  1/ sec^2 A  = cos^2 A  so we have

cos^2 A . Tan^2 A

 =   1

tan^2 A cos^2 A

so the original identity is proved

11 mintues is the naswer