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

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3.Trigonometrical Ratios, Functions and Identities

easy

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

$\frac{{24}}{7}$

Solution

(d) $\sin x + \cos x = \frac{1}{5}$

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

$\sin 2x = \frac{{ – 24}}{{25}}$

==> $\cos 2x = \frac{{ – 7}}{{25}}$

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

Standard 11

Mathematics

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