Question

If$\tan n \theta = \tan m \theta$, then the different values of $\theta$will be in.

• A. A.P.
• B. G.P.
• C. H.P.
• D. None of these

Answer 1

Answer: (A)

A.P.

Answer 2

We have $\tan n \theta = \tan m \theta$ $\Rightarrow$ $n \theta = N \pi + ( m \theta )$

$\Rightarrow$ $\theta = \frac { N \pi } { n - m }$, putting $N = 1,2,3 \ldots \ldots \ldots$ we get

which are obviously in A.P.

Since common difference $d = \frac { \pi } { n - m }$.