If \(\sin^2 A - \cos^2 A = \dfrac{1}{4}\), then find the value of \(\cos^2 A\).
\(\dfrac{3}{8}\)
Step 1 – Use the identity \(\sin^2 A + \cos^2 A = 1\):
\(\sin^2 A = 1 - \cos^2 A\).
Step 2 – Substitute into the given equation:
\((1 - \cos^2 A) - \cos^2 A = \dfrac{1}{4}\)
\(1 - 2\cos^2 A = \dfrac{1}{4}\)
\(2\cos^2 A = 1 - \dfrac{1}{4} = \dfrac{3}{4} \implies \cos^2 A = \dfrac{3}{8}\).
Hence, the correct answer is \(\dfrac{3}{8}\).
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