**Summary**

Remember these derivatives of the trigonometric functions:

#### Differentiation of *sin(x) and cos(x)*

To begin with, we know that differentiation is a method to find the gradient of a curve.

Rule of differentiation is if , then . However in this article we will focus entirely on differentiation of trigonometric functions.

Consider the graph of in the range . We draw tangents to the sin curve at the points where radians.

x | 0 | ||||

sin(x) | 0 | 1 | 0 | -1 | 0 |

We now plot the values of the gradients of these tangents and we obtain a graph of *cos(x)*. As shown in Fig 2.

Hence, this shows that derivative of *sin(x)* is *cos(x)*. It can be written as:

when x in radians.

Similarly, we can find that:

#### Differentiation of *tan(x)*

Let’s assume ,

using quotient rule

#### Differentiation of *sec(x)*

Let’s assume: ,

#### Differentiation of *cosec(x)*

Assume

Taking the derivative:

Hence, to conclude derivatives of trigonometric functions are:

#### Example 1

Q. Differentiate with respect to *x*

*Solution:*

use the identity

**Ans:**