JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

1 of 1

Application +4 | -1

{\tanh ^{ - 1}}\left( {x + iy} \right) = \frac{1}{2}{\tanh ^{ - 1}}\left( {\frac{{2x}}{{1 + {x^2} + {y^2}}}} \right) + \frac{i}{2}{\tan ^{ - 1}}\left( {\frac{{2y}}{{1 - {x^2} - {y^2}}}} \right),\;\,x,\;\,y \in R

, then

{\tanh ^{ - 1}}\left( {iy} \right)

View answer and explanation

Correct option: C

i{\tan ^{ - 1}}y

Option C (

i{\tan ^{ - 1}}y

) is correct because it is derived by substituting

x = 0

into the given equation and simplifying using trigonometric identities.

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\cos ^{-1}(\cos 12)-\sin ^{-1}(\sin 12)

\sin \left(2 \tan ^{-1}(1 / 3)\right)+

\cos \left(\tan ^{-1} 2 \sqrt{2}\right)

\cos ^ {-1}\left\{\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right\}=

\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1

x

{x^2} + {y^2} + {z^2} = {r^2},

{\tan ^{ - 1}}\left( {\frac{{xy}}{{zr}}} \right) + {\tan ^{ - 1}}\left( {\frac{{yz}}{{xr}}} \right) + {\tan ^{ - 1}}\left( {\frac{{xz}}{{yr}}} \right)\;

2{\tan ^{ - 1}}\left( {\frac{1}{3}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right)