SOLUTION
Given the image in the question tab, the following are the solution steps to the answer
Step 1: Write out the function
[tex]\begin{gathered} \sin \theta=\frac{10}{13} \\ \text{since }\sin \theta=\frac{opp}{hyp} \\ \therefore opp=10,\text{ hyp=13} \end{gathered}[/tex]Step 2: Solve for the adjacent using the pythagoras theorem
[tex]\begin{gathered} \text{hyp}^2=opp^2+adj^2 \\ 13^2=10^2+adj^2 \\ \text{adj}^2=13^2-10^2 \\ \text{adj}=\sqrt[]{169-100} \\ \text{adj}=\sqrt[]{69} \end{gathered}[/tex]Step 3: Calculate the value of cos2Ф
[tex]\begin{gathered} cos2\theta=\cos ^2\theta-\sin ^2\theta \\ \cos 2\theta=(\frac{\text{adj}}{\text{hyp}})^2-(\frac{opp}{hyp})^2 \\ \cos 2\theta=(\frac{\sqrt[]{69}}{13})^2-(\frac{10}{13})^2 \\ \cos 2\theta=\frac{69}{169}-\frac{100}{169} \\ \cos 2\theta=-\frac{31}{169} \end{gathered}[/tex]Hence, the value of cos2Ф is -31/169.
