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If tan^{–1} 3 + tan^{–1}x = tan^{–1} 8, then x =

We are given with,

tan^{-1} 3 + tan^{-1} x = tan^{-1} 8

We need to find the value of x.

Using property of inverse trigonometry,

Let us replace A by 3 and B by x.

Since, according to the question

tan^{-1} 3 + tan^{-1} x = tan^{-1} 8

So,

Taking tangent on both sides,

Using property of inverse trigonometry,

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

Now, in order to find x, we need to solve the linear equation.

By cross-multiplying,

⇒ 3 + x = 8(1 – 3x)

⇒ 3 + x = 8 – 24x

⇒ 24x + x = 8 – 3

⇒ 25x = 5

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