Question

cos2A/1+sin2A=tan(π/4-A)

Answer 1

(1 - cos2A)/sin2A = tanA

Use the double-angle formulas:
sin2A = 2sinA cosA
cos2A = cos²A - sin²A = 2cos²A - 1 = 1 - 2sin²A

along with the definition:
tanA = sinA / cosA

EDIT:
Bear in mind that this identity works everywhere except where sin2A = 0; which is:
A = ½nπ
where n = any integer, +, -, or 0.
Note that this also covers values where cosA = 0.

Answer 2

Hello users....

We have to prove that
Cos2A/1+sin2A=tan(π/4-A)

Solution:-
As shown in attachment...

Formula used :
Cos 2x = cos²x- sin²x
Sin²x +cos² x =1
Sin 2x = 2sin x cos x
And
(1-tan x)/(1+tan x) = tan (π/4 -x)

⭐⭐ Hope it helps ⭐⭐