- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
medium
If $a\,\cos 2\theta + b\,\sin 2\theta = c$ has $\alpha$ and $\beta$ as its solution, then the value of $\tan \alpha + \tan \beta $ is
A
$\frac{{c + a}}{{2b}}$
B
$\frac{{2b}}{{c + a}}$
C
$\frac{{c - a}}{{2b}}$
D
$\frac{b}{{c + a}}$
Solution
(b) $a\cos 2\theta + b\sin 2\theta = c$
==> $a\left( {\frac{{1 – {{\tan }^2}\theta }}{{1 + {{\tan }^2}\theta }}} \right) + b\frac{{2\tan \theta }}{{1 + {{\tan }^2}\theta }} = c$
$ \Rightarrow $ $a – a{\tan ^2}\theta + 2b\tan \theta = c + c{\tan ^2}\theta $
$ \Rightarrow $$ – (a + c){\tan ^2}\theta + 2b\,\tan \theta + (a – c) = 0$
$\therefore \tan \alpha + \tan \beta = – \frac{{2b}}{{ – (c + a)}} = \frac{{2b}}{{c + a}}$ .
Standard 11
Mathematics
