Answer: [tex]\cos 2 \theta = \dfrac{-7}{25}[/tex]
Step-by-step explanation:
Given: [tex]\tan \theta = \dfrac{4}{3}[/tex] and [tex]\pi < \theta< \dfrac{3\pi }{2}[/tex]
To find: [tex]\cos 2 \theta[/tex]
Now as we know
[tex]\cos 2x = \dfrac{1- \tan ^2 x}{1+ \tan ^2 x}[/tex]
So we have
[tex]\cos 2 \theta = \dfrac{1-(\dfrac{4}{3} )^2}{1+(\dfrac{4}{3} )^2} \\\\\Rightarrow \cos 2 \theta = \dfrac{1- \dfrac{16}{9} }{1+ \dfrac{16}{9} } = \dfrac{\dfrac{9-16}{9} }{\dfrac{9+16}{9}} = \dfrac{-7}{25}[/tex]
Therefore d. is the correct option
Hence , [tex]\cos 2 \theta = \dfrac{-7}{25}[/tex]
