Prove that \[\sin^7\theta +\cos^7 \theta\] \[=\] \[(\sin\theta +\cos\theta)\left(\sin^4\theta + \cos^4\theta - \frac{(1+\sin\theta +\cos\theta)(\sin\theta +\cos\theta -1)(1-\sin^2\theta \cos^2\theta)}{2} \right) \]

**Note** :- For your proof let \(\sin \theta = s\) and \(\cos \theta =c\)

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