If $\mathop \sum \limits_{i = 1}^{20} {\sin ^{ - 1}}{x_i} = 10\pi ,$ then $\mathop \sum \limits_{i = 1}^{20} {x_i}$ is equal to

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

1 of 1

Analyzing +4 | -1

\sum \limits_{i = 1}^{20} {\sin ^{ - 1}}{x_i} = 10\pi ,

then

\sum \limits_{i = 1}^{20} {x_i}

is equal to

View answer and explanation

Correct option: A

Option A (20) is correct because the maximum value of

{\sin ^{ - 1}}x

\frac{\pi}{2}

. Therefore, each term in the summation must be

\frac{\pi}{2}

, implying each

x_i

is 1.

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)