The idea

Trigonometric identities

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.

A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.

In this lesson — start anywhere

Pure · Trigonometry

Trigonometric identities

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.

Why it works

Two facts in disguise

Two identities do almost all the work at AS, and they're both just facts you already know in disguise. First: $\tan\theta \equiv \dfrac{\sin\theta}{\cos\theta}$ . In a right-angled triangle

\tan = \dfrac{\text{opp}}{\text{adj}}

. Divide top and bottom by the hypotenuse and that's

\dfrac{\text{opp}/\text{hyp}}{\text{adj}/\text{hyp}} = \dfrac{\sin\theta}{\cos\theta}

. It holds for every angle (wherever

\cos\theta \ne 0

Keep reading — free

The rest of the explanation, plus 2 worked examples you step through move by move.

Start free

Takes a minute — no card.