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Identities with Reciprocal Trigonometric Functions (Edexcel A Level Maths): Revision Note

Roger B

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Roger B

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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 Tips and Tricks

  • 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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    Roger B

    Author: Roger B

    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.