Given:
[tex]\sin\theta=\frac{5}{13}[/tex]
Required:
To find the value of
[tex]\cos2\theta[/tex]
Explanation:
We know that
[tex]\cos2\theta=1-2\sin^2\theta[/tex][tex]\begin{gathered} =1-2(\sin\theta)^2 \\ \\ =1-2(\frac{5}{13})^2 \\ \\ =1-2(\frac{25}{169}) \\ \\ =1-\frac{50}{169} \\ \\ =\frac{169-50}{169} \\ \\ =\frac{119}{169} \end{gathered}[/tex]
Final Answer:
[tex]\cos2\theta=\frac{119}{169}[/tex]
