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} $
$\Rightarrow \sin 2 x=\frac{1}{25}-1=\frac{24}{25}$
Now, $\cos 2 x=\sqrt{1-\sin ^{2} 2 x}$
$=\sqrt{1-\frac{576}{625}}=\sqrt{\frac{49}{625}}$
$=-\frac{7}{25}$
$\therefore \tan 2 x=\frac{\sin 2 x}{\cos 2 x}$
$=\frac{-24 / 25}{-7 / 25}=\frac{24}{7}$