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The most general values oro satisfying t...

The most general values oro satisfying `tan theta + tan((3pi)/4+theta)= 2` are

A

`npi+(pi)/(3),ninI`

B

`2npi+(pi)/(3),ninI`

C

`2npi+-(pi)/(3),ninI`

D

`2npi+(-1)^(n)(pi)/(3),ninI`

Text Solution

Verified by Experts

The correct Answer is:
A
Since ,`tantheta+tan((3pi)/(4)+theta)=2`
`thereforetantheta+(-1+tantheta)/(1+tantheta)=2 " "[because"tan"(3pi)/(4)=-1]`
`rArrtantheta+tan^(2)theta-1+tantheta=2+2tantheta`
`rArrtan^(2)theta=3`
`rArrtan^(2)theta=(sqrt(3))^(2)="tan"^(2)(pi)/(3)`
`rArrtheta=npi+(pi)/(3),ninI`
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