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This topic covers the fundamental trigonometric identities — sin²x + cos²x = 1 and tan x = sin x / cos x — and uses them to simplify expressions, prove identities and rewrite equations before solving. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Use sin squared plus cos squared equals 1, and tan equals sin over cos, to rewrite an equation in a single function. Then solve as a quadratic if needed. When proving an identity, work on one side only until it matches the other.
Before you start
Get trig ratios and Pythagoras straight before you begin. Later work on solving equations and proving identities assumes it.
What you learn
Nearly every question needs both identities together. The second lets you turn any tan into a fraction — and once it is a fraction, you can multiply through to clear it. Decide the sign from the given range by picturing the graph — is the curve above or below the axis there? To prove an identity, start on one side (usually the messier one) and work to the other. The course works through the two identities, given one ratio, find the others, proving identities, ‘Show that’ — forming a quadratic and multi-step conversions. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Trig Identities (C12) is a Trigonometry topic in the A-level syllabus, covered here at the AS year. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. It sits alongside Trig Ratios & Exact Values, Addition Formulae, Double Angle Formulae, Further Trig Equations and Inverse Trig Functions in the same strand. For unlimited practice, the Trigonometry revision engine builds new questions on demand and records your accuracy.
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