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The value of sec[tan^(-1)((b+a)/(b-a))-t...

The value of `sec[tan^(-1)((b+a)/(b-a))-tan^(-1)((a)/(b))]` is

A

2

B

`sqrt(2)`

C

`4`

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
`sec[tan^(-1)((b+a)/(b-a))-tan^(-1)((a)/(b))]`
`=sec[tan^(-1){((b+a)/(b-a)-(a)/(b))/(1+((b+a)/(b-a))((a)/(b)))}]`
`=sec[tan^(-1)(1)]="sec"(pi)/(4)=sqrt(2)`.
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