^ −1 x+ ^ −1 1 x + ^ −1 x+ ^ −1 1 x = - Vidyadip

MCQ

$\sin^{−1}\text{x}+\sin^{−1}\frac{1}{\text{x}}+\cos^{−1}\text{x}+\cos^{−1}\frac{1}{\text{x}}=$

✓
$\pi$
B
$2\pi$
C
$ \cfrac{3\pi}{2}$
D
None of these

✓

Answer

Correct option: A.

$\pi$

We know, $ \displaystyle \sin ^{ -1 }{ \theta } +\cos ^{ -1 }{ \theta } =\frac { \pi }{ 2 }$
$\therefore \sin ^{ -1 }{ \text{x} } +\sin ^{ -1 }{ \frac { 1 }{ \text{x} } } +\cos ^{ -1 }{ \text{x} } +\cos ^{ -1 }{ \frac { 1 }{ \text{x} } }$
$ \displaystyle =\frac { \pi }{ 2 } +\frac { \pi }{ 2 } $
$=\pi$

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