Buktikan Cosα=1:tanα

1-sin2A/cos2A=1-tanA/1+tanA
sin 2A = 2 sinA cosA , cos2A = cos ^2 A - sin ^2 A
and sin ^2 A + cos ^2 A = 1
[( cos ^2 A + sin ^2 A - 2sin A cos A ) / ( cos^2 A - sin^2 A) ] =
[ 1 - ( sin A / cos A)] / [ 1 + ( sinA / cos A)]
[ ( cos A - sin A) ^2] / [(cosA - sinA)( cos A + sinA)] = [(cosA - sin A) / cos A] / [ (cos A + sin A ) / cosA]

[(cos A - sin A) / ( cos A + sin A )] = [( cos A - sinA) / cos A] [ cos A / (cos A + sin A) ]

cos 2A / 1+sin 2A=1-tan A / 1+tan A
1 - tan A
------------ =
1 + tan A


1 - sin A/cos A
---------------------
1 + sin A/cos A

Multiply by cos A on top and bottom.

cos A - sin A
------------------
cos A + sin A

Multiply top and bottom both by (cos A + sin A)

(cos A - sin A)(cos A + sin A)
--------------------------------------… =
(cos A + sin A)(cos A + sin A)

cos² A - sin² A
--------------------------------------… =
cos² A + 2sin A cos A + sin² A

cos 2A
--------------------------------------… =
(cos² A + sin² A) + 2sin A cos A


cos 2A
------------- <== answer (left hand side)
1+ sin 2A