Question

Cot^2A(secA_1)/1+sinA=sec^2A(1_sinA/1+secA)

Answer 1

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