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  4. If sin x+ cos x=(1/5), then tan 2 x is

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

Trigonometric Functions

Solution:

$\sin\, x+\cos\, x=\frac{1}{5}$
$\Rightarrow \sin ^{2} x+\cos ^{2} x+2 \sin\,x \cos \,x-\frac{1}{25}$
$\sin \,2 x =\frac{-24}{25} \Rightarrow \cos \,2 x =\frac{-7}{25} \Rightarrow \tan \,2 x =\frac{24}{7}$