Respuesta :
[tex]\cos 2(\text { theta })=\frac{7}{25}[/tex]
[tex]\tan 2(\text { theta })=-\frac{24}{7}[/tex]
Step-by-step explanation:
Given data:
[tex]\tan \theta=-\frac{3}{4}[/tex]
To find:
cos 2 theta and tan 2 theta
Solution:
Hence, the trigonometric formula for those are below,
[tex]\tan 2(\text { theta })=\frac{2 \tan (\text { theta })}{1-\tan ^{2}(\text { theta })}[/tex]
[tex]\cos 2(\text { theta })=\frac{1-\tan ^{2}(\text { theta })}{1+\tan ^{2}(\text { thet } a)}[/tex]
Now, find the required data by substituting the given value. We get,
[tex]\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}[/tex]
Similarly for cos 2 theta,
[tex]\cos 2(\text { theta })=\frac{1-\frac{9}{16}}{1+\frac{9}{16}}=\frac{7}{16} \times \frac{16}{25}=\frac{7}{25}[/tex]
