List of Pythagorean Identities
As we know the three basic Pythagorean identities in trigonometry are:
- sin2θ + cos2θ = 1
- 1 + tan2θ = sec2θ
- 1 + cot2θ = cosec2θ
Variation of Pythagorean Identities
However, from these identities we can derive the other six identities as well, which are given by:
- sin2θ + cos2θ = 1
- 1 – cos2θ = sin2θ
- 1 – sin2θ = cos2θ
- 1 + tan2θ = sec2θ
- sec2θ – tan2θ = 1
- tan2θ = sec2θ – 1
- 1 + cot2θ = cosec2θ
- cosec2θ – cot2θ = 1
- cot2θ = cosec2θ – 1
Pythagorean Identities
Pythagorean Identities in trigonometry are derived from Pythagorean Theorem. They are also called Pythagorean Trigonometric Identities. One of the basic Pythagorean identity is sin²θ + cos²θ = 1. Let’s learn more about, Pythagorean identities in trigonometry including their proof and solved examples, as well.
Table of Content
- What are Pythagorean Identities?
- Pythagorean Trig Identities
- List of Pythagorean Identities
- Variation of Pythagorean Identities
- Pythagorean Identities Derivation
- Derivation of sin2θ + cos2θ = 1
- Derivation of 1 + tan2θ = sec2θ
- Derivation of 1 + cot2θ = cosec2θ
- FAQs