- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
medium
If $\tan \,(A - B) = 1,\,\,\,\sec \,(A + B) = \frac{2}{{\sqrt 3 }},$ then the smallest positive value of $B$ is
A
$\frac{{25}}{{24}}\pi $
B
$\frac{{19}}{{24}}\pi $
C
$\frac{{13}}{{24}}\pi $
D
$\frac{{11}}{{24}}\pi $
Solution
(b) $\tan (A – B) = 1 \Rightarrow A – B = \frac{\pi }{4}$…..(i)
and $\sec (A + B) = \frac{2}{{\sqrt 3 }} \Rightarrow A + B = \frac{{11\pi }}{6}$…..(ii)
from (i) and (ii),
$ \Rightarrow B = \frac{{19\pi }}{{24}}$.
Standard 11
Mathematics
