Example Question 1

Example corresponding to question 1 in trigonometry_1.

Example 1


$\tan \theta - \cot \theta =$

  1. $2 \sec \theta$

  2. $\dfrac{1-2 \sin^2 \theta}{\dfrac{1}{2} \sin \theta}$

  3. $\dfrac{1-2 \sin^2 \theta}{\sin 2 \theta}$

  4. $\dfrac{1-2 \cos^2 \theta}{\dfrac{1}{2} \sin 2 \theta}$

  5. $\dfrac{1-2 \sin^2 \theta}{\dfrac{1}{2} \sin 2 \theta}$

Solution


  1. We first use the identities $\tan \theta = \dfrac{\sin \theta}{\cos \theta}$ and $\cot \theta = \dfrac{\cos \theta}{\sin \theta}$ to rewrite the given expression as follows:

    $\tan \theta - \cot \theta = \dfrac{\sin \theta}{\cos \theta} - \dfrac{\cos \theta}{\sin \theta}$

    $=\dfrac{\sin^2 \theta - \cos^2 \theta}{\sin \theta \cos \theta}$

  2. We now use the identities $\sin^2 \theta = 1 - \cos^2 \theta$ and $\dfrac{1}{2} \sin 2\theta = \sin \theta \cos \theta$ to rewrite the given expression as follows

    $=\dfrac{}{}

    Answer A