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If tan x=(a)/(b) and tan 2x=(b)/(a+b) fi...

If `tan x=(a)/(b)` and `tan 2x=(b)/(a+b)` find the smallest positive value of x.

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Verified by Experts

The correct Answer is:
`tan^(-1)(1)/(3)`
`tan 2x=(b)/(a+b)`
`rArr(2tanx)/(1-tan^(2)x)=(b)/(a+b)`
`rArr((2a)/(b))/(b-a)=b`
`rArr(2ab)/(b-a)=b`
`rArr2a=b-a`
`rARr 3a=b`
`rArr (a)/(b)=(1)/(3)`
now, `tan x=(a)/(b)`
`rArr x=tan^(-1)""(1)/(3)`.
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