Question

If tan theta= -3/4 and θ is in quadrant IV, cos2 theta= and tan2 theta= .

Answer 1

$\cos 2(\text { theta })=\frac{7}{25}$

$\tan 2(\text { theta })=-\frac{24}{7}$

Step-by-step explanation:

Given data:

               $\tan \theta=-\frac{3}{4}$

To find:

           cos 2 theta and tan 2 theta

Solution:

Hence, the trigonometric  formula for those are below,

                    $\tan 2(\text { theta })=\frac{2 \tan (\text { theta })}{1-\tan ^{2}(\text { theta })}$

                    $\cos 2(\text { theta })=\frac{1-\tan ^{2}(\text { theta })}{1+\tan ^{2}(\text { thet } a)}$

Now, find the required data by substituting the given value. We get,

                    $\tan 2(\text { theta })=\frac{2 \times\left(-\frac{3}{4}\right)}{1-\frac{9}{16}}=-\frac{3}{2} \times \frac{16}{7}=-\frac{24}{7}$

Similarly for cos 2 theta,

                  $\cos 2(\text { theta })=\frac{1-\frac{9}{16}}{1+\frac{9}{16}}=\frac{7}{16} \times \frac{16}{25}=\frac{7}{25}$