draw the graph of 4sin(x+30) and 2+tanx for values of x from 0 degree to 360degree and obtain the solution within the range of the equation 4sin(x+30)-tan x=2

I can't draw it for you.

We can't draw graphs for you, but you will get the solution(s) to your equation where the two curves intersect.

That is because, when
4sin(x+30) = 2+tanx ,

4sin(x+30) -tan x = 2

Assume the 30 is in degrees.

Sample calculations:
when x = 0, 4sin(x+30) = 2.000
and 2 + tanx = 2
That is one solution already!

To draw the graph of 4sin(x+30) and 2+tanx, we can follow these steps:

1. Start by creating a table of values for the given equations. We will calculate values of sin(x+30), tan(x), 4sin(x+30), and 2+tan(x) for values of x ranging from 0 degrees to 360 degrees.

| x | sin(x+30) | tan(x) | 4sin(x+30) | 2+tan(x) |
|:---:|:---------:|:------:|:----------:|:--------:|
| 0 | 0.5 | 0 | 2 | 2 |
| 30 | 1 | 0.577 | 4 | 2.577 |
| 60 | 0.5 | 1.732 | 2 | 3.732 |
| ... | ... | ... | ... | ... |
| 360 | 0.5 | 0 | 2 | 2 |

2. Plot the points obtained from the table on a graph, with x-values along the x-axis and y-values along the y-axis. Connect the points with a smooth curve.

3. The graph of 4sin(x+30) will have a periodic nature, repeating itself after every 360 degrees. It will oscillate between the maximum value of 4 and the minimum value of -4. The graph will be shifted to the left by 30 degrees due to the "+30" inside the parentheses.

4. The graph of 2+tanx will also have a periodic nature, repeating every 180 degrees. For values of x where tan(x) is not defined (such as x = 90, 270), we can use limits to determine the value of 2+tanx.

5. To find the solution within the given range for the equation 4sin(x+30) - tanx = 2, we need to look for the points where the graphs of 4sin(x+30) and 2+tanx intersect. These intersection points will give the x-values where the equation holds true.

By following these steps, you can draw the graph and find the solution within the range of the equation.