| { | |
| "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 $\\sin 2 \\theta = \\boxed{\\frac{9}{16}}.$" | |
| } |