If $\tan \theta=\frac{1}{3}$, then $\cos 2 \theta=$

If $\tan \theta=\frac{1}{3}$, then $\cos 2 \theta=$
  1. $\frac{1}{4}$
  2. $\frac{1}{10}$
  3. $\frac{1}{5}$
  4. $\frac{4}{5}$

Solution

$\cos 2 \theta=\frac{1-\tan ^{2} \theta}{1+\tan ^{2} \theta}=\frac{\left(1-\frac{1}{9}\right)}{\left(1+\frac{1}{9}\right)}=\frac{4}{5}$

Asked in: MHT CET 2020 (13 Oct Shift 1)

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