Question

Total number of solutions of the equation 3x + 2 tan x = in x [0, 2] is equal to

- 1
- 2
- 3
- 4

Hint:

### Here, we have given is 3x + 2 tanx = . We have to find how many solutions it has. Firstly, separate the tanx. And draw the graph for tanx and find the intersection point this equation. The intersection point is solution It given region to [ 0, 2π].

## The correct answer is: 1

### Here we have to find the how many solutions it has.

Firstly, the equation is

3x + 2 tanx =

2tanx = – 3x

tanx = – 3/2 x

let y = tanx ; y = – x

Now using graph,

At x = 0, y =

And at y = 0, x =

Given region of graph is [ 0, 2π ] .

Hence, according to graph it intersects = 3 so it has 3 number of solutions

Therefore, the correct answer is 3

In this question, we use the graph of tanx . The intersection is the total number of solutions of this equation. The graph region is [ 0, 2π ].

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