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tan^(-1)(C(1)x-y)/(c(1)+c(3)c(2))+..+tan...

`tan^(-1)(C_(1)x-y)/(c_(1)+c_(3)c_(2))+..+tan^(-1)(1)/(c_(n))` is equal top

A

`tan^(-1)(y)/(x)`

B

`tan^(-1)(x/y)`

C

`-tan^(-1)(x)/(y)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`tan^(-1)((c_(1)x-y)/(c_(1)y+x))+tan^(-1)(c_(2)-c_(1)/(12+c_(2)c_(1))+tan^(-1)(c_(3)-c_(2))/(1+c_(3)c_(2))+…+tan^(-1)(1)/(c_(n))`
`=tan^(-1)(x)/(y)-tan^(-1)(1)/(c_(1))+(tan^(-1)(1)/(c_(1))-tan^(-1)(1)/(c_(2))+(tan^(-1))(1)/(c_(2))-tan^(-1)(1)/(c_(3))+..+(tan^(-12))(1)/(c_(n-1))-tan^(-1)(1)/(c_(n)))+tan^(-1)(1)/(c_(n))`
`=tan^(-1)(x)/(y)`
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