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Prove that tan^(-1)(2/11)+tan^(-1)(7/24...

Prove that `tan^(-1)(2/11)+tan^(-1)(7/24)=tan^(-1)(1/2)`

A

1

B

`(1)/(sqrt(3))`

C

`sqrt(3)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `"tan"^(-1)(2)/(11)+"tan"^(-1)(7)/(24)="tan"^(-1){((2)/(11)+(7)/(24))/(1-(2)/(11)xx(7)/(24))}`
`[becausetan^(-1)x+tan^(-1)y=tan^(-1)((x+y)/(1-xy)),]`
`=tan^(-1){(48xx77)/(264-14)}=tan^(-1){(125)/(250)}=tan^(-1){(1)/(2)}`
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