MCQ
If $\sin x + \cos x = \frac{1}{5},$ then $\tan 2x$ is
  • A
    $\frac{{25}}{{17}}$
  • B
    $\frac{{7}}{{25}}$
  • C
    $\frac{{25}}{7}$
  • $\frac{{24}}{7}$

Answer

Correct option: D.
$\frac{{24}}{7}$
d
(d) $\sin x + \cos x = \frac{1}{5}$

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

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

==> $\cos 2x = \frac{{ - 7}}{{25}}$ 

==> $\tan 2x = \frac{{24}}{7}$.

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