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8. Sequences and Series
medium
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
Solution
(a) We have $\tan n\theta = \tan m\theta $
$ \Rightarrow $$n\theta = N\pi + (m\theta )$
$ \Rightarrow $ $\theta = \frac{{N\pi }}{{n – m}}$,
putting $N = 1,\;2,\;3………,$ we get
$\frac{\pi }{{n – m}},\;\frac{{2\pi }}{{n – m}},\;\frac{{3\pi }}{{n – m}}………$
which are obviously in $A.P.$
Since common difference $d = \frac{\pi }{{n – m}}$.
Standard 11
Mathematics
