Explanation
We are given the following:
[tex]\cos\theta=\frac{12}{37}[/tex]
We are required to determine the value of cos 2Θ.
We know that the double angle identity states:
[tex]\begin{gathered} \cos2\theta=2\cos^2\theta-1 \\ where \\ \cos^2\theta=(\cos\theta)^2 \end{gathered}[/tex]
Therefore, we can evaluate cos 2Θ as:
[tex]\begin{gathered} \cos\text{ }2\theta=2\cos^2\theta-1 \\ \cos\text{ }2\theta=2(\cos\theta)^2-1 \\ \cos2\theta=2(\frac{12}{37})^2-1 \\ \cos2\theta=2(\frac{144}{1369})-1 \\ \cos2\theta=\frac{288}{1369}-1 \\ \cos2\theta=-\frac{1081}{1369} \end{gathered}[/tex]
Hence, the answer is:
[tex]\cos2\theta=-\frac{1081}{1369}[/tex]
