Discussion
What is the value of (sin15°+cos15°)2+(sin15°-cos15°)2 ?
Answer: B
The value is 2.
Expand both squares; the cross terms cancel:
\[ \begin{aligned} (s + c)^{2} + (s - c)^{2} &= 2s^{2} + 2c^{2} \\ &= 2(\sin^{2}15^\circ + \cos^{2}15^\circ) \\ &= 2 \times 1 = 2 \end{aligned} \]
Here \(s = \sin 15^\circ\) and \(c = \cos 15^\circ\). The \(+2sc\) from the first square and the \(-2sc\) from the second cancel, so the angle does not matter at all. 1 forgets the factor 2: it is the value of \(\sin^{2} + \cos^{2}\) alone. 0 and \(-1\) are impossible, since a sum of two squares cannot be zero or negative here.
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