`sin^(10)x+cos^(10)x=29/16cos^4 2x`

Explanation

To solve the equation \( \sin^{10} x + \cos^{10} x = \frac{29}{16} \cos^4 2x \), we can follow these steps:

### Step 1: Rewrite the left-hand side using half-angle identities
We know that:
\[ \sin^2 x = \frac{1 - \cos 2x}{2} \quad \text{and} \quad \cos^2 x = \frac{1 + \cos 2x}{2} \]
Thus, we can express \( \sin^{10} x \) and \( \cos^{10} x \) as:
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