train/precalculus/1068.json

{
    "problem": "If $\\cos \\theta + \\sin \\theta = \\frac{5}{4},$ then find $\\sin 2 \\theta.$",
    "level": "Level 2",
    "type": "Precalculus",
    "solution": "Squaring the equation, we get\n\\[\\cos^2 \\theta + 2 \\cos \\theta \\sin \\theta + \\sin^2 \\theta = \\frac{25}{16}.\\]Then $\\sin 2 \\theta + 1 = \\frac{25}{16},$ so $\\sin 2 \\theta = \\boxed{\\frac{9}{16}}.$"
}