- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
medium
$\frac{{\tan A + \sec A - 1}}{{\tan A - \sec A + 1}} = $
A
$\frac{{1 - \sin A}}{{\cos A}}$
B
$\frac{{1 - \cos A}}{{\sin A}}$
C
$\frac{{1 + \sin A}}{{\cos A}}$
D
$\frac{{1 + \cos A}}{{\sin A}}$
Solution
(c) $\frac{{\tan A + \sec A – 1}}{{\tan A – \sec A + 1}}$
$ = \frac{{\sin A – \cos A + 1}}{{\sin A – 1 + \cos A}} $
$= \frac{{\sin A + (1 – \cos A)}}{{\sin A – (1 – \cos A)}}$
$ = \frac{{2\sin \frac{A}{2}\cos \frac{A}{2} + 2{{\sin }^2}\frac{A}{2}}}{{2\sin \frac{A}{2}\cos \frac{A}{2} – 2{{\sin }^2}\frac{A}{2}}}$
$ = \frac{{\cos \frac{A}{2} + \sin \frac{A}{2}}}{{\cos \frac{A}{2} – \sin \frac{A}{2}}} $
$= \frac{{{{\left( {\cos \frac{A}{2} + \sin \frac{A}{2}} \right)}^2}}}{{{{\cos }^2}\frac{A}{2} – {{\sin }^2}\frac{A}{2}}}$
$ = \frac{{1 + \sin A}}{{\cos A}}$.
Standard 11
Mathematics
