Question

If $\sin x+\cos x=\frac{1}{5}$, then $\tan 2x$ is
$(\frac{\pi }{2}<x<\frac{3\pi }{4})$

• A. $\frac{-24}{7}$
• B. $\frac{7}{25}$
• C. $\frac{25}{7}$
• D. $\frac{24}{7}$

Answer 1

The correct option is D $\frac{24}{7}$

$\sin x+\cos x=\frac{1}{5}$
On squaring we get,

$1+2\sin x\cos x=\frac{1}{25}$

$\Rightarrow \sin 2x=-\frac{24}{25}$

$\Rightarrow \cos 2x=\sqrt{1-{\sin }^{2}2x}$

$\Rightarrow \cos 2x=\sqrt{1-\frac{576}{625}}$

$\therefore \cos 2x=-\frac{7}{25}$ as $2x$ is in III${}^{rd}$ quadrant.

$\Rightarrow \tan 2x=\frac{sin2x}{cos2x}=\frac{24}{7}$