[tex] cos^{2}x = 1- sin^{2} x \\ sinx = \frac{24}{25} \\ \\ cosx = \sqrt{1-sin^{2}x } \Rightarrow cosx = \sqrt{1- (\frac{24}{25})^{2} } \Rightarrow cosx = \sqrt{1- \frac{576}{625} } \Rightarrow \\ \Rightarrow cosx = \sqrt{ \frac{625-576}{625} } \Rightarrow cosx = \sqrt{ \frac{49}{625} } \Rightarrow cosx = \frac{7}{25} [/tex]
