The trigonometric identities are the equations which are valid for the right-angled triangles. The trigonometric ratios are the basic identities in trigonometry which are applied throughout the concept.

The fundamental identities of trigonometry are as follows:

To obtain additional trigonometric identities, we use **Pythagoras theorem**.

## Pythagoras Theorem statement:

**“In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.”**

From the image above, we have

c²=a²+b² (1)

Divide throughout equation (1) by c².

Let us write trigonometric ratios for the image given above. Assume angle to be θ.

Substitute sine and cosine values in equation (2).

**Remember!
**

Using the result obtained from Pythagoras theorem + =1, we get the following identities.

**Complementary Angle Identities**

Each of the six trigonometric functions is the same as its complementary angle co-function.

When angle θ is reduced to half, we get θ/2. Identities for half angles are as follows.

**Angle Sum, Difference, and Product Identities
**

All the above identities holds good for only right-angled triangles. There are certain identities that hold for all triangles. The identities are as follows.

Consider the triangle shown below.

The above equation can be rearranged as cos C =

The identities are applied to prove many equations. Let us learn some of the examples and understand the applications of these identities learnt so far.

**Example 3: Find the value of the following.
**

**Solution:** 3θ can be written as 2θ + θ.

Know more about other concepts of Trigonometry on What is Trigonometry – An Introduction and Trigonometric Ratios

**Online Math Classes > Math Concepts > Trigonometry > Trigonometric Identities**