Problem
\( (2 \sin x+\cos x)^{2}+(2 \cos x-\sin x)^{2}=5 \)
Solution
Step 1 ：\( (2 \sin x + \cos x)^2 + (2 \cos x - \sin x)^2 = (2 \sin x)^2 + 2 \cdot 2 \sin x \cdot \cos x + (\cos x)^2 + (2 \cos x)^2 - 2 \cdot 2 \sin x \cdot \cos x + (\sin x)^2 \)
Step 2 ：\( = 4 (\sin x)^2 + 4 (\cos x)^2 + (\sin x)^2 + (\cos x)^2 \)
Step 3 ：\( = 5 (\sin^2 x + \cos^2 x) \)
