Mixed Exercise 10: Trigonometric Identities and Equations | 第10章混合练习：三角恒等式与方程

📚 Mixed Exercise 10: Trigonometric Identities and Equations | 第10章混合练习：三角恒等式与方程

Mixed Exercise 10 brings together the key techniques from the trigonometric identities and equations chapter. You need to recall exact values, apply the two core identities, and solve equations in a given interval without losing solutions. This article breaks the exercise down into focused revision points.

第10章混合练习整合了三角恒等式与方程一章的核心技巧。你需要熟记特殊角的精确值，应用两个基本恒等式，并在给定区间内解方程而不丢失解。本文把该练习拆解为几个重点复习模块。

1. The Big Picture: What Mixed Exercise 10 Tests | 全局概览：混合练习10考查什么

Mixed Exercise 10 typically contains a mixture of proof and equation-solving. The examiner checks whether you can choose the correct identity, rewrite an expression, and find all solutions in the interval, usually 0° ≤ θ ≤ 360° or 0 ≤ θ ≤ 2π.

混合练习10通常包含证明与解方程两类题。考官要检验你是否会选择正确的恒等式、能否重写表达式，并在给定区间（常见 0° ≤ θ ≤ 360° 或 0 ≤ θ ≤ 2π）内找出所有解。

Questions often combine exact values from the 30°, 45°, 60° family with sign rules from the four quadrants.

题目常把30°、45°、60°一族的精确值与四个象限的正负号规则结合起来考查。

The exercise also includes equations that become quadratics in sin θ or cos θ, so algebraic factorising is as important as trig knowledge.

练习中还包含可化为 sin θ 或 cos θ 二次型的方程，因此代数因式分解与三角知识

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