AQA A Level Maths: Pure复习笔记5.5.3 Trigonometry - Further Identities

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


Exam 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