Answer:
-7/25
Step-by-step explanation:
Disclaimer: I'm using variable x instead of theta.
Step 1: Simplify cos 2x.
[tex] \cos(2x) = \cos {}^{2} (x) - { \sin {}^{2} (x) }^{2} [/tex]
[tex] \cos(2x) = \cos {}^{2} (x) - (1 - \cos {}^{2} (x) ) [/tex]
[tex]2 \cos {}^{2} (x) - 1[/tex]
We know that cos x= 3/5 so that means
[tex] 2(\frac{3}{5} ){}^{2} - 1 = 2( \frac{9}{25} ) - 1 = \frac{18}{25} - 1 = \frac{ - 7}{25} [/tex]
So the exact value of cos 2x=
[tex] \frac{ - 7}{25} [/tex]
There is another way to find this but this is easier.
