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tan^(-1)(x/y)-tan^(-1)(x-y)/(x+y)is equa...

`tan^(-1)(x/y)-tan^(-1)(x-y)/(x+y)`is equal to(A) `pi/2` (B) `pi/3` (C) `pi/4` (D) `(-3pi)/4`

A

`(pi)/(2)`

B

`(pi)/(3)`

C

`(pi)/(4)`

D

`(-3pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
C
` tan^(-1)""((x)/(y))-tan^(-1)""((x-y)/(x+y))`
`tan^(-1)""(x)/(y)-tan^(-1)(((x)/(y)-1)/((x)/(y)+1))`
`tan^(-1)""(x)/(y)-(tan^(-1)""(x)/(y)-tan^(-1)""1)`
`=tan^(-1)1=(pi)/(4)`
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