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