Let us take a right angled triangle with hypotenuse length 1. If we mark one of the acute angles as θ, then using the definition of the sine ratio, we have
As the hypotenuse is 1,
Repeating the same process using the definition of the cosine ratio, we have
Since this is a right triangle, we can use the Pythagorean Theorem:
This is the most fundamental identity in trigonometry.
From this identity, if we divide through by squared cosine, we are left with:
If instead we divide the original identity by squared sine, we are left with:
There are basically 3 main trigonometric identities. The proofs
come directly from the definitions of these functions and the
application of the Pythagorean theorem:
Angle SumDifference Identities
Quiz: Lesson_3:Trigonometric_Identities_quiz
