CIE A Level Maths: Pure 3复习笔记3.1.3 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