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Question: \(\sum_{i = 1}^{1000}{\sin^{- 1}x_{i}}\) = 500 p then value of \(\sum_{i = 1}^{1000}x_{i}\)...

∑i=11000sin⁡−1xi\sum_{i = 1}^{1000}{\sin^{- 1}x_{i}} = 500 p then value of ∑i=11000xi\sum_{i = 1}^{1000}x_{i}

A

500

B

100

C

100000

D

1000

Answer

1000

Explanation

Solution

cos q = 1/x, tan q = sin⁡θcos⁡θ\frac{\sin\theta}{\cos\theta}=1−(1/x)21/x\frac{\sqrt{1 - (1/x)^{2}}}{1/x}

= x2−1\sqrt{x^{2} - 1}