Show that `2(sin^6x+cos^6x)-3(sin^4x+cos^4x)+1=0`.

Explanation

To show that \( 2(\sin^6 x + \cos^6 x) - 3(\sin^4 x + \cos^4 x) + 1 = 0 \), we will follow these steps:

### Step 1: Rewrite \(\sin^6 x + \cos^6 x\)
Using the identity for the sum of cubes, we can rewrite \(\sin^6 x + \cos^6 x\):
\[ \sin^6 x + \cos^6 x = (\sin^2 x + \cos^2 x)(\sin^4 x - \sin^2 x \cos^2 x + \cos^4 x) \]
Since \(\sin^2 x + \cos^2 x = 1\), we have:
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