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The number of solutions of the equation is

We need to find the number of solutions of the equation,

We shall apply the property of inverse trigonometry, that is,

So,

Taking tangent on both sides of the equation,

Using property of inverse trigonometry,

tan(tan^{-1} A) = A

Also,

We get,

Simplifying it,

⇒ 5x = 1 – 6x^{2}

⇒ 6x^{2} + 5x – 1 =0

Since, this is a quadratic equation, it is clear that it will have 2 solutions.

Let us check:

We have,

6x^{2} + 5x – 1 = 0

⇒ 6x^{2} + 6x – x – 1 = 0

⇒ 6x(x + 1) – (x + 1) = 0

⇒ (6x – 1)(x + 1) = 0

⇒ (6x – 1) = 0 or (x + 1) = 0

⇒ 6x = 1 or x = -1

Hence, there are 2 solutions of the given equation.

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