If \(\sin A + \cos A = x\), then find the value of \(\sin^2 A + \cos^2 A + 2\sin A \cos A\).
\(x^2\)
Recognise the expression as a perfect square:
\(\sin^2 A + \cos^2 A + 2\sin A \cos A = (\sin A + \cos A)^2\).
Since \(\sin A + \cos A = x\):
\((\sin A + \cos A)^2 = x^2\).
Hence the value is \(x^2\).
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