If $tan^{-1} 3 + tan^{-1}x = tan^{-1}8,$

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Inverse Trigonometric Functions

Question:

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

Options:

$\frac{1}{5}$

$\frac{5}{14}$

$\frac{14}{5}$

Correct Answer:

$\frac{1}{5}$

Explanation:

we have,

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

$⇒tan^{-1} x = tan^{-1}8- tan^{-1}3$

$⇒tan^{-1} x = tan^{-1}\left(\frac{8-3}{1+24}\right) ⇒x =\frac{1}{5}$