Question

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

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

Answer 1

Answer: (B)

Given that, $\sin x+\cos x=\frac{1}{5}$
On squaring both sides, we get
${\sin }^{2}x+{\cos }^{2}x+2\sin x\cos x=\frac{1}{25}$
$\Rightarrow \sin 2x=\frac{1}{25}-1=\frac{24}{25}$
Now, $\cos 2x=\sqrt{1-{\sin }^{2}2x}$
$=\sqrt{1-\frac{576}{625}}=\sqrt{\frac{49}{625}}$
$=-\frac{7}{25}$
$\therefore \tan 2x=\frac{\sin 2x}{\cos 2x}$
$=\frac{-24/25}{-7/25}=\frac{24}{7}$