Pure · Trigonometry
Chapter 1 · 3
The idea
The sec/cosec/cot identities
The two new Pythagorean identities 1 + tan²θ ≡ sec²θ and 1 + cot²θ ≡ cosec²θ — deriving them from sin²+cos²≡1, and using them to prove identities, simplify expressions and turn equations into a solvable quadratic.
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
The sec/cosec/cot identities
The two new Pythagorean identities 1 + tan²θ ≡ sec²θ and 1 + cot²θ ≡ cosec²θ — deriving them from sin²+cos²≡1, and using them to prove identities, simplify expressions and turn equations into a solvable quadratic.
Why it works
One identity you already own
Here is the problem this page solves. Exam questions now mix the new functions with the old ones — an equation likehas a and a in it, and you can't solve for two different functions at once. You need a bridge between them. The good news: you already own the only identity that matters, — and both bridges on this page are just that identity in disguise.
Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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