If the equation contains trig functions with the same angle and some of them are squared then it may be possible to use a Pythagorean identity to write an equation in the same trig. function which may then possibly factorise.

In these examples I show you how the Pythagorean identities help solve some equations.

Pythagorean Identities:

  • sin2θ + cos2θ ≡ 1
  • 1 + tan2θ ≡ sec2θ
  • 1 + cot2θ ≡ cosec2θ

Example 1

Example 2

Example 3