Home
Class 12
MATHS
If tan^(-1)a+tan^(-1)b+tan^(-1)c=pi, th...

If `tan^(-1)a+tan^(-1)b+tan^(-1)c=pi`, then which of the following is true ?

A

`a+b-c=(ab)/(c)`

B

`a+b+c=abc`

C

`a+b+c=1`

D

abc =1

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `tan^(-1)a+tan^(-1)b+tan^(-1)x=pi`
`rArrtan^(-1)((a+b)/(1-ab))+tan^(-1)x=pi`
`rArrtan^(-1)(((a+b)/(1-ab)+c)/(1-(a+b)/(1-ab)))=pi`
`rArr((a+b)/(1-ab)+c)/(1-(a+b)/(1-ab)*c)=tan^(-1)pi=0`
`rArra+b+c-abc=0`
`rArra+b+c=abc`
Promotional Banner

Similar Questions

Explore conceptually related problems

If tan ^(-1)x+tan^(-1)y-sin^(-1)x=0, then which of the following are true?

Which of the following is true? tan 1>tan^(-1)1

If tan A=(1)/(2) and tan B=(1)/(3) , then which of the following is true ?

If tan^(-1)a + tan^(-1)b + tan^(-1)c= sin^(-1)1 , then

If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y . Then which of the following may be true

If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y . Then which of the following may be true (A) (x+y)/(tan1)=-2 (B) (tan^(-1)x)/(1-tan^(-1)y)=2 (C) (x+y)/(tan1)=2 (D) (x+y)/(cot1)=1

If tan alpha=3 and tan beta=(1)/(2) , then which of the following is true ?

tan^(-1)a+tan^(-1)b=(pi)/(2)

If tan ^(-1)a+tan^(-1)b+tan^(-1)c=pi then prove tjhat a+b+c=abc