Solution
$$cos^{4}A-sin^{4}A$$ = ( $$cos^{2}A-sin^{2}A$$ ) ( $$cos^{2}A+sin^{2}A$$)
We know that, $$cos^{2}A - sin^{2}A$$ = cos 2(A)
and $$cos^{2}A + sin^{2}A$$ = 1
Therefore,
$$cos^{4}A-sin^{4}A$$ = cos2A
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