Inverse trigonometry #1

Geometry Level 3

tan ⁡ − 1 ( x + 1 x − 1 ) + tan ⁡ − 1 ( x − 1 x ) = tan ⁡ − 1 ( − 7 ) \tan^{-1}\left(\dfrac{x+1}{x-1}\right) + \tan^{-1}\left(\dfrac{x-1}{x}\right)=\tan^{-1}\left( -7\right)

Find the number of solution(s) of the above equation.

None of these 0 0 2 2 1 1

Akshat Sharda by Akshat Sharda , 21, India

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1 solution

Info Web
Sep 29, 2020

LHS is pi + tan^-1 (-7) (since the product (3)(1/2)>1) and not tan^-1 (-7) when x=2 is put. Hence, NO Solutions Exist

The reason x=2 is the only solution to be checked is because on adding the LHS and simplifying, we get tan^-1 (2x^2-x+1/1-x) which equals tan^-1 (-7);

(2x^2-x+1)/(1-x) = -7, solving the quadratic we get x=2.

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