Trigonometric Proof (DP IB Analysis & Approaches (AA)): Revision Note

Trigonometric proof

What identities might I have to use during a proof?

• You are given the following identities in the SL section of the formula booklet

  • Identity for

    • 

  • Pythagorean identity

    • 

  • Double angle identities

    • 

    • 

• You are given the following identities in the HL section of the formula booklet

  • Reciprocal trigonometric identities

    • 

    • 

  • Pythagorean identities

    • 

    • 

  • Compound angle identities

    • 

    • 

    • 

  • Double angle identity for tan

    • 

• You are not given the following identities and need to remember them

  • Reciprocal trigonometric identity for cot

    • 

  • Identity for

    • 

How do I prove an identity?

• To prove an identity:

  • Select one side to start on

    • It is more common to start on the left-hand side

    • However, you can start on the right-hand side

  • Apply relevant identities to turn that expression into the one on the other side

What should I look out for when proving trigonometric identities?

• Check to see if any of the angles are double or half any of the others

  • You can use the double angle identities

    • e.g. you can replace  with 

    • e.g. you can replace with 

    • e.g. you can replace with

• Check to see if any of the terms have an even power

  • You can use the Pythagorean identities

    • e.g. you can replace with

• Check to see if any terms can cancel

  • e.g. you can replace with to cancel the 1 in the expression

• Combine any fractions

  • e.g. rewrite as

• Always keep an eye on the 'target' expression – this can help suggest what identities to use