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 $cosx+sinx=\frac{1}{2}$
$\Rightarrow 1+sin2x=\frac{1}{4}$ (By squaring both sides)
$\Rightarrow \frac{2tanx}{1+ta{n}^{2}x}=\frac{-3}{4}$
$\Rightarrow 3ta{n}^{2}x+8tanx+3=0$
$\therefore tanx=\frac{-8\pm \sqrt{64-36}}{6}$
$=\frac{-4\pm \sqrt{7}}{3}$