A LevelMaths: PureAQARevision Notes5. Trigonometry5.5 Reciprocal & Inverse Trigonometric Functions5.5.3 Trigonometry - Further Identities

Trigonometry - Further Identities (AQA A Level Maths: Pure)

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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

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

Examiner Tip

  • These identities are not given in the exam formulae booklet – you have to know them.
  • If you forget them (or forget where the '+1' goes) you can always derive them from sin2x + cos2x ≡ 1 as shown above.
  • Unless told otherwise, you can assume sin2x + cos2x ≡ 1 in any proofs involving sec, cosec or cot on the exam.

Worked example

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

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    Roger

    Author: Roger

    Expertise: Maths

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.