- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
medium
$\frac{{\tan {{70}^o} - \tan {{20}^o}}}{{\tan {{50}^o}}} = $
A
$1$
B
$2$
C
$3$
D
$0$
Solution
(b) $\frac{{\tan {{70}^o} – \tan {{20}^o}}}{{\tan {{50}^o}}}$
$= \frac{{\frac{{\sin {{70}^o}}}{{\cos {{70}^o}}} – \frac{{\sin {{20}^o}}}{{\cos {{20}^o}}}}}{{\frac{{\sin {{50}^o}}}{{\cos {{50}^o}}}}}$
$= \frac{{\frac{{\sin {{70}^o}\cos {{20}^o} – \cos {{70}^o}\sin {{20}^o}}}{{\cos {{70}^o}\cos {{20}^o}}}}}{{\frac{{\sin {{50}^o}}}{{\cos {{50}^o}}}}}$
$= \frac{2}{2} \times \frac{{\sin ({{70}^o} – {{20}^o})\cos {{50}^o}}}{{\cos {{70}^o}\cos {{20}^o}\sin {{50}^o}}}$
$= \frac{{2\sin {{50}^o}\cos {{50}^o}}}{{2\cos {{70}^o}\cos {{20}^o}\sin {{50}^o}}}$
$= \frac{{2\cos {{50}^o}}}{{\cos {{90}^o} + \cos {{50}^o}}}$
$= \frac{{2\cos {{50}^o}}}{{0 + \cos {{50}^o}}}$
$= 2.$
Standard 11
Mathematics
