The general solution of equation `3 tan(theta - 15^o) = tan(theta+15^o)` is:

Options

A. `theta=npi -(pi) /3`
B. `theta=n pi +(pi)/3`
C. `theta=npi -(pi)/4`
D. `theta-npi +(pi)/4`

Answer

D

Explanation

Given `3 tan(theta-15)=tan(theta+15)`
`(tanA)/(tanB)=3/1`,
where `A=theta+15^(@)`
`B=theta-15^(@)`
`implies(tanA+tanB)/(tanA-tanB)=(3+1)/(3-1)`
(Applying componendo and dividendo)
`implies(sin (A+B))/(sin(A-B))=2`
`implies sin 2 theta=2 sin 30^(@)`
`impliessin 2 theta=2 1/2 =1= "sin"(pi)/2`
`implies2 theta=2n pi+(pi)/2`
`implies n pi=npi+(pi)/4`