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<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Trigonometric Formulas</title>
    <style>
        body {
            font-family: Arial, sans-serif;
            background-color: #f4f4f9;
            margin: 0;
            padding: 20px;
            color: #333;
        }
        h1, h2 {
            text-align: center;
            color: #007BFF;
        }
        .container {
            max-width: 800px;
            margin: 0 auto;
            padding: 20px;
            background: #fff;
            border-radius: 10px;
            box-shadow: 0 4px 8px rgba(0, 0, 0, 0.1);
        }
        section {
            margin-bottom: 20px;
        }
        .formula {
            padding: 10px 15px;
            background: #f9f9f9;
            border-left: 4px solid #007BFF;
            margin: 10px 0;
            font-family: "Courier New", monospace;
        }
        footer {
            text-align: center;
            margin-top: 30px;
            color: #777;
            font-size: 0.9em;
        }
    </style>
</head>
<body>
    <h1>Trigonometric Formulas</h1>
    <div class="container">
        <!-- Basic Ratios -->
        <section>
            <h2>Basic Trigonometric Ratios</h2>
            <div class="formula">sin(θ) = Opposite / Hypotenuse</div>
            <div class="formula">cos(θ) = Adjacent / Hypotenuse</div>
            <div class="formula">tan(θ) = Opposite / Adjacent = sin(θ) / cos(θ)</div>
            <div class="formula">csc(θ) = 1 / sin(θ)</div>
            <div class="formula">sec(θ) = 1 / cos(θ)</div>
            <div class="formula">cot(θ) = 1 / tan(θ)</div>
        </section>

        <!-- Pythagorean Identities -->
        <section>
            <h2>Pythagorean Identities</h2>
            <div class="formula">sin²(θ) + cos²(θ) = 1</div>
            <div class="formula">1 + tan²(θ) = sec²(θ)</div>
            <div class="formula">1 + cot²(θ) = csc²(θ)</div>
        </section>

        <!-- Angle Sum and Difference Formulas -->
        <section>
            <h2>Angle Sum and Difference Formulas</h2>
            <div class="formula">sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)</div>
            <div class="formula">cos(A ± B) = cos(A)cos(B) ∓ sin(A)sin(B)</div>
            <div class="formula">tan(A ± B) = (tan(A) ± tan(B)) / (1 ∓ tan(A)tan(B))</div>
        </section>

        <!-- Double Angle Formulas -->
        <section>
            <h2>Double Angle Formulas</h2>
            <div class="formula">sin(2A) = 2sin(A)cos(A)</div>
            <div class="formula">cos(2A) = cos²(A) - sin²(A)</div>
            <div class="formula">tan(2A) = 2tan(A) / (1 - tan²(A))</div>
        </section>

        <!-- Half-Angle Formulas -->
        <section>
            <h2>Half-Angle Formulas</h2>
            <div class="formula">sin(A/2) = ±√((1 - cos(A)) / 2)</div>
            <div class="formula">cos(A/2) = ±√((1 + cos(A)) / 2)</div>
            <div class="formula">tan(A/2) = ±√((1 - cos(A)) / (1 + cos(A)))</div>
        </section>

        <!-- Product-to-Sum Formulas -->
        <section>
            <h2>Product-to-Sum Formulas</h2>
            <div class="formula">sin(A)sin(B) = ½[cos(A-B) - cos(A+B)]</div>
            <div class="formula">cos(A)cos(B) = ½[cos(A+B) + cos(A-B)]</div>
            <div class="formula">sin(A)cos(B) = ½[sin(A+B) + sin(A-B)]</div>
        </section>

        <!-- Sum-to-Product Formulas -->
        <section>
            <h2>Sum-to-Product Formulas</h2>
            <div class="formula">sin(A) + sin(B) = 2sin((A+B)/2)cos((A-B)/2)</div>
            <div class="formula">sin(A) - sin(B) = 2cos((A+B)/2)sin((A-B)/2)</div>
            <div class="formula">cos(A) + cos(B) = 2cos((A+B)/2)cos((A-B)/2)</div>
            <div class="formula">cos(A) - cos(B) = -2sin((A+B)/2)sin((A-B)/2)</div>
        </section>

        <!-- Law of Sines and Cosines -->
        <section>
            <h2>Law of Sines and Cosines</h2>
            <div class="formula">Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)</div>
            <div class="formula">Law of Cosines: c² = a² + b² - 2ab cos(C)</div>
        </section>
    </div>
    <footer>
        &copy; 2024 Trigonometry Guide. All Rights Reserved.
    </footer>
</body>
</html>