Respuesta :

Solution:

Given;

[tex]\sin(A)=-\frac{4}{5}[/tex]

Then, the value of cosine x is;

[tex]\cos(A)=-\frac{3}{5}[/tex]

Because cosine and sine are negative on the third quadrant.

Then;

[tex]\begin{gathered} \cos(2A)=\cos^2(A)-\sin^2(A) \\ \\ \cos(2A)=(-\frac{3}{5})^2-(-\frac{4}{5})^2 \\ \\ \cos(2A)=\frac{9}{25}-\frac{16}{25} \\ \\ \cos(2A)=-\frac{7}{25} \end{gathered}[/tex]

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