ASMaths: Pure 2CIERevision Notes3. Trigonometry3.1 Reciprocal Trigonometric Functions3.1.3 Trigonometry - Further Identities

Trigonometry - Further Identities (CIE AS Maths: Pure 2)

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Trigonometry - Further Identities

What identities do I need to know with secant, cosecant, and cotangent?

  • There are two identities with sec, cosec and cot that you need to know and be able to use:
    • tan2x + 1 ≡ sec2x
    • 1 + cot2x ≡ cosec2x
  • These are not really 'new' identities – they can both be derived from sin2x + cos2x ≡ 1
    • To derive the identity for sec2x  divide  sin2x + cos2x ≡ 1  by cos2x
    • To derive the identity for cosec2x  divide  sin2x + cos2x ≡ 1  by sin2x

Trig Fur IDs Illustr 1, A Level & AS Maths: Pure revision notes

Examiner Tip

  • These identities are given in the exam formulae booklet – make sure you know how to find them. 
  • They will be needed to prove some trigonometric identities and solve some trigonometric equations.

Worked example

Trig Fur IDs Example, A Level & AS Maths: Pure revision notes

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    Lucy

    Author: Lucy

    Expertise: Head of STEM

    Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels. Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all. Lucy has created revision content for a variety of domestic and international Exam Boards including Edexcel, AQA, OCR, CIE and IB.