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Solve for x: tan^(-1)3x+tan^(-1)2x=pi/4...

Solve for x: `tan^(-1)3x+tan^(-1)2x=pi/4`

A

1 and 6

B

`-1` and 6

C

`1and(1)/(6)`

D

`-1and(1)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
D
`tan^(-1)3x+tan^(-1)2x=(pi)/(4)`
`rArrtan^(-1)((3x+2x)/(1-3xxxx2x))=(pi)/(4)[because"tan"^(-1)x+tan^(-1)y=tan^(-1)((x+y)/(1-xy))]`
`rArrtan^(-1)((5x)/(1-6x^(2)))=(pi)/(4)`
`rArr(5x)/(1-6x^(2))="tan"(pi)/(4)[becausetan^(-1)(theta)=phirArrtheta=tanphi]`
`rArr(5x)/(1-6x^(2))=1`
`rArr5x=1-6x^(2)`
`rArr6x^(2)+5x-1=0`
`rArr6x^(2)+6x-x-1=0`
`rArr6x(x+1)-1(x+1)=0`
`rArr(6x-1)(x+1)=0`
`rArr6x-1=0`
and x + 1=0
`rArrx=(1)/(6)`
and x=-1
Hence , required value of x is `(1)/(6) and -1`.
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