Loading...
Two identities underpin almost all of trigonometry at this level: the Pythagorean identity and the tangent identity. They let you rewrite expressions, prove results and turn awkward equations into ones you can solve.
What you'll be able to do
The Pythagorean identity comes straight from the unit circle (it is Pythagoras in disguise). The tangent identity is the definition of .
Tip — Rearranged forms are just as useful: sin²θ = 1 − cos²θ and cos²θ = 1 − sin²θ.
Spotting where an identity applies turns a messy expression into something simple. Look especially for groupings.
To prove an identity, start with one side (usually the messier one) and manipulate it using the two identities until it equals the other side. Never move terms across the .
Tip — When you see 1 − cos²θ or 1 − sin²θ, immediately replace it with sin²θ or cos²θ.
Formula recap
Common mistakes to avoid
Key takeaways
Test yourself
Ready to lock in Trigonometric Identities? Pick a mode and earn XP & Dobloons.
Real past-paper questions on Trigonometric Identities, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.
19 marks · 5 papers — pulled from past papers and marked mark‑by‑mark, so what you miss feeds straight into your weak‑topic list.