# What is the slope of the line normal to the tangent line of #f(x) = xcotx+2xsin(x-pi/3) # at # x= (15pi)/8 #?

##### 1 Answer

#### Explanation:

For reference :-

As slope of any line is the derivative of the equation, I will differentiate the equation of tangent.

clearly,

Here I can see the trigonometric formula of

Solving,

by above 2 formulas, I get,

So, at

The value of above equation becomes

Now, at

Now, when a line is normal to the tangent line, it means that the line is perpendicular to the tangent line.

Let the slope of perpendicular line be

If the lines are perpendicular to each other then,

So, using above equation the slope of line normal to the tangent comes out to be,

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