Question

If $0 < x < \pi$ and $cosx + sinx = 1/2$, then $tanx$ is

• A. $\frac{\left(1-\sqrt{7}\right)}{4}$
• B. $\frac{\left(4-\sqrt{7}\right)}{3}$
• C. $\frac{-4 \pm\sqrt{7}}{3}$
• D. $\frac{\left(1+\sqrt{7}\right)}{4}$

Answer 1

Answer: (C)

$0 < x < \pi$ and $cosx + sinx =\frac{1}{2}$
$\Rightarrow 1+sin\,2x=\frac{1}{4}$ (By squaring both sides)
$\Rightarrow \frac{2\,tan\,x}{1+tan^{2}\,x}=\frac{-3}{4}$
$\Rightarrow 3tan^{2}\,x+8tan\,x+3=0$
$\therefore tan\,x=\frac{-8 \pm\sqrt{64-36}}{6}$
$=\frac{-4 \pm\sqrt{7}}{3}$