A-level · Trigonometry

Trigonometric identitiesExam-style questions

The two AS identities — tan ≡ sin/cos and sin²+cos² ≡ 1 — where they come from, and how to use them to simplify expressions and prove "show that" results.

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8 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4

1
Show that $\tan^2 x - \sin^2 x \equiv \sin^2 x \tan^2 x$ .
Level 3 · 3 marksTry it
2
Show that $\dfrac{\sin\theta}{1 + \cos\theta} + \dfrac{1 + \cos\theta}{\sin\theta} \equiv \dfrac{2}{\sin\theta}$ .
Level 3 · 3 marksTry it