Saved Bookmarks
| 1. |
If \( \sum_{i=1}^{300} \cos ^{-1} x_{i}=0 \). Then find the value of \( \sum_{i=1}^{300} \sin ^{-1} x_{i} \) (1) 0 (2) \( 150 \pi \) (3) 150 (4) \( 151 \pi \) |
|
Answer» Correct option is (2) 150π \(\sum^{300}_{i =1} cos^{-1}x_i = 0\) (Given) \(\therefore\sum^{300}_{i =1} \left(\frac{\pi}{2} - sin^{-1}x_i\right)= 0\) \(\left(\because cos^{-1}x = \frac{\pi}{2} - sin^{-1}x\right)\) ⇒ \(\frac{\pi}{2}\times 300 - \sum^{300}_{i =1}sin^{-1}x_i = 0\) \(\left(\because \sum^{300}_{i = 1} = 300\right)\) ⇒ \(\sum^{300}_{i = 1 }sin^{-1}x_i = 150 \pi\) |
|