If x + x = 1 5 , then 2x is - Vidyadip

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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