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The number of solution of the equation 2...

The number of solution of the equation `2sin^(-1)((2x)/(1+x^(2)))-pi x^(3)=0` is equal to

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
D
We have 2 `sin^(-1)((2x)/(1+x^(2)))-pi x^(3)=0`
or `sin^(-1)((2x)/(1+x^(2)))=(pi)/(2)x^(3)`
Now we know that
`sin^(-1)((2x)/(1+x^(2)))={{:(-2 tan^(-1)x-pi",",xlt -1),(2 tan^(-1)x",",-1le x le 1),(-2 tan^(-1)x+pi",",x gt 1):}`
To find the number of solution of the equation, we draw the graph of `y=sin^(-1)((2x)/(1+x^(2)))` and `y=(pi)/(2)x^(3)`

Clearly, there are 3 solutions of the equation `{-1,0,1}`.
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