Question

If $\sin x+\cos x=\frac{1}{5}$, then $\tan 2x$ is

• A. $\frac{25}{17}$
• B. $\frac{7}{25}$
• C. $\frac{25}{7}$
• D. $\frac{24}{7}$

Answer 1

Answer: (D)

$\sin x+\cos x=\frac{1}{5}$
$\Rightarrow {\sin }^{2}x+{\cos }^{2}x+2\sin x\cos x-\frac{1}{25}$
$\sin 2x=\frac{-24}{25}\Rightarrow \cos 2x=\frac{-7}{25}\Rightarrow \tan 2x=\frac{24}{7}$