RS Aggarwal// Trigonometric Identities// Ex... 8B 1to 5
Channel: Physics world 247
Date: 2023-06-28

RS Aggarwal// Trigonometric Identities// Ex... 8B 1to 5
Trigonometric identities are equations that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified.

Here are some of the most common trigonometric identities:

* Pythagorean identities:
    * sin² θ + cos² θ = 1
    * 1 + tan² θ = sec² θ
    * cosec² θ = 1 + cot² θ
* Sum and difference identities:
    * sin (α + β) = sin α cos β + cos α sin β
    * sin (α - β) = sin α cos β - cos α sin β
    * cos (α + β) = cos α cos β - sin α sin β
    * cos (α - β) = cos α cos β + sin α sin β
* Double angle identities:
    * sin 2θ = 2 sin θ cos θ
    * cos 2θ = cos² θ - sin² θ = 2 cos² θ - 1 = 1 - 2 sin² θ
    * tan 2θ = (2 tan θ) / (1 - tan² θ)
* Triple angle identities:
    * sin 3θ = 3 sin θ - 4 sin³ θ
    * cos 3θ = 4 cos³ θ - 3 cos θ
    * tan 3θ = (3 tan θ - tan³ θ) / (1 - 3 tan² θ)

These are just a few of the many trigonometric identities that exist. There are many other identities that can be used to simplify trigonometric expressions. If you are interested in learning more about trigonometric identities, there are many resources available online and in libraries.

Here are some books that you may find helpful:

* **Trigonometry by Michael Sullivan**
* **Trigonometry by Ron Larson**
* **Trigonometry by James Stewart**

I hope this helps!