If \(\sin A + \csc A = 2\), then the value of \(\sin^2 A + \csc^2 A\) is:
Answer: B
Let \(x = \sin A\). Then \(\csc A = 1/x\). We are given \(x + 1/x = 2\). This is only possible if x=1. So, \(\sin A = 1\).
Then \(\csc A = 1/\sin A = 1\).
The expression becomes \(\sin^2 A + \csc^2 A = 1^2 + 1^2 = 1 + 1 = 2\).
Alternatively, square the given equation: \((\sin A + \csc A)^2 = 2^2\).
\(\sin^2 A + \csc^2 A + 2\sin A \csc A = 4\).
Since \(\sin A \csc A = 1\), we have \(\sin^2 A + \csc^2 A + 2 = 4\).
\(\sin^2 A + \csc^2 A = 2\).