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  "body": "\n## Statement\n\nFor every real $x$,\n$$\\sin^2 x + \\cos^2 x = 1.$$\n\n## Remarks\n\nLet $f(x) = \\sin^2 x + \\cos^2 x$. By the [[derivatives|00R4MWW532]] [[of sine and cosine|0V2DV29EGT]], $f'(x) = 2 \\sin x \\cos x - 2 \\cos x \\sin x = 0$. So $f$ is [[constant|003QDZ4T16]], and $f(0) = 1$.\nSo $|\\sin x| \\le 1$ and $|\\cos x| \\le 1$.\nGeometrically, the point $(\\cos x, \\sin x)$ lies on the unit circle. Mathlib states it as `Real.sin_sq_add_cos_sq`.\n\n## Explanations\n\n### L1 human\n\nIn a right triangle with hypotenuse $1$, the legs are $\\cos x$ and $\\sin x$.\nThe Pythagorean theorem then says that their squares add up to $1$.\n",
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