If `3tan(theta-15^0)=tan(theta+15^0),` then `theta` is equal to `n in Z)` n`pi+pi/4` (b) `npi+pi/8` `npi+pi/3` (d) none of these

Options

A. `n pi+pi/4`
B. `n pi+pi/8`
C. `n pi+pi/3`
D. none of these

Answer

A

Explanation

Let `A = theta +15^(@), B=theta-15^(@)`
`rArr A+B=2 theta and A-B=30^(@)`
Now `(tan A)/(tan B)=3/1`
or `(tan A+tan B)/(tan A- tan B)=(3+1)/(3-1)`
(applying componendo and dividendo rule)
or `(sin (A+B))/(sin (A-B))=2`
`rArr sin 2theta=2 sin 30^(@)=1`
`rArr 2 theta=2n pi +pi/2 or theta =n pi +pi/4 n in Z`