The value of `3(sinx-cosx)^(4)+6(sinx+cosx)^(2)+4(sin^(6)xcos^(6)x)` is

Explanation

To solve the expression \(3(\sin x - \cos x)^4 + 6(\sin x + \cos x)^2 + 4(\sin^6 x + \cos^6 x)\), we will break it down step by step.

### Step 1: Simplify \((\sin x - \cos x)^4\)

We can express \((\sin x - \cos x)^4\) as \(((\sin x - \cos x)^2)^2\).

Using the identity \((a - b)^2 = a^2 - 2ab + b^2\):

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