Question

In a $\Delta ABCif\tan A<0$ , then

• A. $\mathrm{tanBtanC}>1$
• B. $\mathrm{tanBtanC}<1$
• C. $\mathrm{tanBtanC}=1$
• D. NONE OF THESE

Answer 1

Answer: (B)

$\mathrm{tanBtanC}<1$

$A+B+C={180}^{\circ }$

as $tanA<0$

$\therefore \frac{\pi }{2}<A<\pi$

hence $0<B+C<\frac{\pi }{2}$

or $tan(B+C)<tan\left(\frac{\pi }{2}\right)$

or $\frac{1}{tan(B+C)}>\frac{1}{tan\frac{\pi }{2}}$

$\frac{1-tanBtanC}{tanB+tanC}>0$

as $tanB,tanC=+ve$

$\therefore 1-tanBtanC>0$

or $tanBtanC<1$