Total number of solutions of the equation 3x+2tan⁡x=5π2 in x∈[0,2π] is equal to

# Total number of solutions of the equation  is equal to

1. A

1

2. B

2

3. C

3

4. D

4

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### Solution:

We have, $3\mathrm{x}+2\mathrm{tan}\mathrm{x}=\frac{5\mathrm{\pi }}{2}$

Let   $\frac{5\mathrm{\pi }}{4}-\frac{3\mathrm{x}}{2}=\mathrm{y}$

and  $\mathrm{y}=\mathrm{tan}\mathrm{x}$

$\therefore$times in $\left[0,2\mathrm{\pi }\right]$.Thus,

the number of solutions of given equation is 3.

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