Identities with Reciprocal Trigonometric Functions (Edexcel IAL Maths)

Trigonometry - Further Identities

Spec point — 2.2

Identities with reciprocal trigonometric functions

What are the reciprocal trigonometric identities?

• There are two identities with sec,cosec and cot that you need to know and be able to use:

  • tan²**x + 1 ≡ sec²x
  • 1 + cot²x ≡ cosec**²x

• 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

Exam Hint

• These identities are not 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