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cosA + sinA = root 2cosA [given]
( cosA + sinA)^2= 2 cos^2A
cos^2A + sin^2A + 2 sinA cosA = 2 cos^2A
1+ 2 sinA cosA = 2 cos^2A
or 2 sinA cosA = 2 cos^2A -1
now cosA - sinA = sqrt[ (cosA+ sinA)^2 - 4 sinA cosA ]
= sqrt[ 2 cos^2A -2( 2os^2A - 1)
=sqrt2 sqrt [ cos^2A - 2cos^2A +1 ]
=sqr2 sqrt[ 1- cos^2A]
= sqrt2 sinA PROVED
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