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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
If $\sin x+\cos x=\frac{1}{5}$, then $\tan 2 x$ is
  • A
    $\frac{25}{17}$
  • B
    $\frac{7}{25}$
  • C
    $\frac{25}{7}$
  • ✓
    $\frac{24}{7}$
✓

Answer

Correct option: D.
$\frac{24}{7}$
(D)
$\sin x+\cos x=\frac{1}{5}$
$\Rightarrow \sin ^2 x+\cos ^2 x+2 \sin x \cos x=\frac{1}{25}$
$\Rightarrow \sin 2 x=\frac{-24}{25} \Rightarrow \cos 2 x=\frac{-7}{25}$
$\Rightarrow \tan 2 x=\frac{24}{7}$

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