ત્રિકોણ ABC માં , tan A + tan B + tan C = 6 અને tan Atan B = 2, તો tan

English

Gujarati

Hindi

3.Trigonometrical Ratios, Functions and Identities

medium

ત્રિકોણ $ABC$ માં , $\tan A + \tan B + \tan C = 6$ અને $\tan A\tan B = 2,$ તો $\tan A,\,\,\tan B$ અને $\tan C$ મેળવો.

A

$1, 2, 3$

B

$2,1,3$

C

$(a)$ અને $(b)$ બંને

D

એકપણ નહિ.

Solution

(c) $\tan A + \tan B + \tan C = \tan A\tan B\tan C$

$\therefore \tan A\tan B\tan C = 6 \Rightarrow \tan C = \frac{6}{2} = 3$

Also $\tan A + \tan B = 6 – 3 = 3$

$\therefore \tan A,\tan B = 2,1$ or $1, 2$ and $\tan C = 3$.

Standard 11

Mathematics

Share

Similar Questions

$\sin \frac{\pi }{{14}}\sin \frac{{3\pi }}{{14}}\sin \frac{{5\pi }}{{14}}\sin \frac{{7\pi }}{{14}}\sin \frac{{9\pi }}{{14}}\sin \frac{{11\pi }}{{14}}\sin \frac{{13\pi }}{{14}} = . . . .$

medium

(IIT-1991)

જો $\tan A = \frac{{1 – \cos B}}{{\sin B}},$ હોય તો $\tan 2A$ અને $\tan B$ નો સંબંધ મેળવો..

easy

(IIT-1983)

જો $\alpha ,\,\beta ,\,\gamma \in \,\left( {0,\,\frac{\pi }{2}} \right)$, તો $\frac{{\sin \,(\alpha + \beta + \gamma )}}{{\sin \alpha + \sin \beta + \sin \gamma }} = . . ..$

easy

$2\,{\sin ^2}\beta + 4\,\,\cos \,(\alpha + \beta )\,\,\sin \,\alpha \,\sin \,\beta + \cos \,2\,(\alpha + \beta ) = $

medium

(IIT-1977)

$\frac{{\sin {{81}^o} + \cos {{81}^o}}}{{\sin {{81}^o} – \cos {{81}^o}}}$=

normal