If \(\sin^2 A - \cos^2 A = \dfrac{{1}}{{2}}\), find the value of \(\cos^2 A\).
\(1/4\)
Using \(\sin^2 A = 1 - \cos^2 A\):
\((1 - \cos^2 A) - \cos^2 A = \dfrac{{1}}{{2}}\)
\(1 - 2\cos^2 A = \dfrac{{1}}{{2}}\)
\(2\cos^2 A = \dfrac{{1}}{{2}} \implies \cos^2 A = \mathbf{{\dfrac{{1}}{{4}}}}\)
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