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3.Trigonometrical Ratios, Functions and Identities
medium
$(m + 2)\sin \theta + (2m - 1)\cos \theta = 2m + 1,$ if
A
$\tan \theta = \frac{3}{4}$
B
$\tan \theta = \frac{4}{3}$
C
$\tan \theta = \frac{{2m}}{{{m^2} + 1}}$
D
None of these
Solution
(b) Squaring the given relation and putting $\tan \theta = t,$
${(m + 2)^2}\,{t^2} + 2(m + 2)\,(2m – 1)t + {(2m – 1)^2} = {(2m + 1)^2}\,(1 + {t^2})$
$ \Rightarrow \,3\,(1 – {m^2})\,{t^2} + (4{m^2} + 6m – 4)\,t – 8m = 0$
$ \Rightarrow \,(3t – 4)\,[(1 – {m^2})\,t + 2m] = 0$,
which is true, if $t = \tan \theta = \frac{4}{3}$ or $\tan \theta = \frac{{2m}}{{{m^2} – 1}}$.
Standard 11
Mathematics
