Find the largest positive integer $n$ such that
\[\sin^n x + \cos^n x \ge \frac{1}{n}\]for all real numbers $x.$
Question:
Find the largest positive integer $n$ such that
\[\sin^n x + \cos^n x \ge \frac{1}{n}\]for all real numbers $x.$
Answer:
Let's think step by step.

user
8
Find the largest positive integer $n$ such that
\[\sin^n x + \cos^n x \ge \frac{1}{n}\]for all real numbers $x.$
train