📚 Example 7.3.2: Solving Trigonometric Equations with Double-Angle Identities | 示例7.3.2：用二倍角公式求解三角方程
Example 7.3.2 is a classic A-level pure mathematics problem that combines the double-angle formula for cosine with the skill of solving a quadratic trigonometric equation. In this article, we will walk through the problem step by step and explain the reasoning behind each move.
示例7.3.2是一道经典的A-level纯数题目，它将余弦的二倍角公式与求解二次三角方程的能力结合起来。本文将一步步带你处理该问题，并解释每一步背后的道理。
1. The Problem | 一、问题
Question: Solve the equation cos 2x + 3 sin x = 2 for 0 ≤ x ≤ 2π. Give your answers in radians.
题目： 解方程cos 2x + 3 sin x = 2，其中0 ≤ x ≤ 2π，答案用弧度表示。
This question appears as Example 7.3.2 in many AQA-style revision exercises. It requires you to recognise that the presence of both cos 2x and sin x suggests using the version of cos 2x that contains only sin x.
这道题以示例7.3.2的形式出现在许多AQA风格的复习练习中。你需要意识到方程同时含有cos 2x和sin x，因此应使用只含sin x的cos 2x展开形式。
2. Key Identity | 二、核心恒等式
The double-angle formula for cosine has three common forms:
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