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If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(...

If `sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2)`, then the value of `sum((x^(101)+y^(101))(x^(202)+y^(202)))/((x^(303)+y^(303))(x^(404)+y^(404)))` is

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
D
Given , `sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2)`
`rArrsin^(-1)x=sin^(-1)y=sin^(-1)z=(pi)/(2)`
`rArrx=y=z=1`
`thereforesum((x^(101)+y^(101))(x^(202)+y^(202)))/((x^(303)+y^(303))(x^(404)+y^(404)))=sum((1+1)(1+1))/((1+1)(1+1))`
`=sum1=3`
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