If x,y and z are in A.P and ${\tan ^{ - 1}}x,\,\,{\tan ^{ - 1}}y\,\,\,\,{\rm{and}}\,\,\,{\tan ^{ - 1}}z$ are also in AP, then

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

1 of 1

Analyzing +4 | -1

If x,y and z are in A.P and

{\tan ^{ - 1}}x,\,\,{\tan ^{ - 1}}y\,\,\,\,\mathrm{and}\,\,\,{\tan ^{ - 1}}z

are also in AP, then

View answer and explanation

Correct option: A

x = y = z

Option A (

x = y = z

) is correct because if x, y, z are in both A.P. and their arctangents are in A.P., it implies they must be equal.

Practice All Chapter MCQs →

\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)