b) $\tan^2 \theta - \sec^2 \theta$

d) $\sin^2 \theta - \cos^2 \theta$

Question

b) $\tan^2 \theta - \sec^2 \theta$

d) $\sin^2 \theta - \cos^2 \theta$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Trigonometric Identities", "Pythagorean Identities" ], "current_concepts": [ "Trigonometric Identities", "Pythagorean Identities" ] } ## 简化表达式 b $$ \begin{aligned} &\sec^2 \theta = 1 + \tan^2 \theta \ &\tan^2 \theta - \sec^2 \theta = \tan^2 \theta - (1 + \tan^2 \theta) = -1 \end{aligned} $$ ## 简化表达式 d $$ \begin{aligned} &\cos(2\theta) = \cos^2 \theta - \sin^2 \theta \ &\sin^2 \theta - \cos^2 \theta = -\cos(2\theta) \end{aligned} $$ ## Question b $-1$ ## Question d $-\cos(2\theta)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Trigonometric Identities" ] }

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Explanation:

简化表达式 b

简化表达式 d

Answer:

Question b

Question d