Q186 / 270 · NDA 2018 (Phase 2) · Mathematics

What is $\frac{2 \tan \theta}{1+\tan ^2 \theta}$ equal to?

  • A
    $\cos 2 \theta$
  • B
    $\tan 2 \theta$
  • Correct answer
    C
    $\sin 2 \theta$
  • D
    $\operatorname{cosec} 2 \theta$

Solution

$\begin{aligned} & \frac{2 \tan \theta}{1+\tan ^2 \theta}=\frac{2 \tan \theta}{\sec ^2 \theta} \\ & =2 \tan \theta \cdot \cos ^2 \theta \\ & =2 \sin \theta \cdot \cos \theta=\sin 2 \theta\end{aligned}$

Hence, the correct answer is option: 'C'.

Relevant Questions