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If x gt y gt 0, then find the value of t...

If `x gt y gt 0`, then find the value of `tan^(-1).(x)/(y) + tan^(-1) [(x + y)/(x -y)]`

A

`(pi)/(4)`

B

`(pi)/(4)`

C

`(3pi)/(4)`

D

none of these

Text Solution

Verified by Experts

`tan^(-1)(x)/(y)+tan^(-1)(x+y)/(x-y)`
`tan^(-1)(x)/(y)+tan^(-1)(1+(x)/(y))/((x)/(y)-1)`
`tan^(-1)(x)/(y)-tan^(-1)(1+(x)/(y))/(1-(x)/(y))`
`tan^(-1)(x)/(y)-(-pi+tan^(-1)1+tan^(-1)(x)/(y))`
`=pi-(pi)/(4)=(3pi)/(4)`
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OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Chapter Test
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