If tan ,nθ = tan mθ , then different values of θ will be in

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8. Sequences and Series

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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

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