A) \[\frac{25}{17}\]
B) \[\frac{24}{7}\]
C) \[\frac{7}{25}\]
D) \[\frac{25}{7}\]
Correct Answer: B
Solution :
Given that, \[\sin x+\cos x=\frac{1}{5}\] On squaring both sides, we get \[{{\sin }^{2}}x+{{\cos }^{2}}x+2\sin x\cos x=\frac{1}{25}\] \[\Rightarrow \] \[\sin 2x=\frac{1}{25}-1=\frac{24}{25}\] Now, \[\cos 2x=\sqrt{1-{{\sin }^{2}}2x}=\sqrt{1-\frac{576}{625}}\] \[=\sqrt{\frac{49}{625}}=-\frac{7}{25}\] \[\therefore \] \[\tan 2x=\frac{\sin 2x}{\cos 2x}=\frac{-24/25}{-7/25}=\frac{24}{7}\]
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