lightbulb Key Concepts

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1. Fundamental Identities

• sin² θ + cos² θ = 1
• 1 + tan² θ = sec² θ
• 1 + cot² θ = cosec² θ

2. Derived Identities

• sec² θ - tan² θ = 1
• cosec² θ - cot² θ = 1
• sin θ = cos(90° - θ)

3. Applications

These identities are used to transform one trigonometric expression into another and to prove various mathematical theorems. Always try to convert expressions to sin and cos for easier simplification.