Solve the equation `sin^(4)x + cos^(4)x =7/2 sinx.cosx.`

Explanation

To solve the equation \( \sin^4 x + \cos^4 x = \frac{7}{2} \sin x \cos x \), we can follow these steps:

### Step 1: Rewrite the Left-Hand Side
We can use the identity for \( a^4 + b^4 \):
\[ a^4 + b^4 = (a^2 + b^2)^2 - 2a^2b^2 \]
Let \( a = \sin x \) and \( b = \cos x \). Thus,
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