If sin theta = -5/7 , which of the following are possible?A) cos theta = √24/7 , and tan theta = 5/√24B) cos theta = -√24/7, and tan theta = 5/√24C) sec theta = 7/√24 , and tan theta = -5/√24 D)sec theta = -7/5, and tan theta = 5/√24

Solution:we are given that[tex] sin \theta=-5/7  [/tex]As we know that [tex] cos \theta =\sqrt{1-sin^2 \theta}  \\ [/tex]Substitute the value we get[tex] cos \theta=\sqrt{1-(\frac{-5}{7})^2}  \\ \\ cos \theta=\sqrt{1-(\frac{25}{49})}  \\ \\ cos \theta=\sqrt{(\frac{24}{49})} =\frac{\sqrt{24}}{7}\\   [/tex]Since [tex] sec \theta=\frac{1}{cos \theta}\\  [/tex]So here [tex] sec \theta=\frac{7}{\sqrt{24}}\\  [/tex]As we know that [tex] tan \theta=\frac{sin \theta}{cos \theta}\\ \\  \text{Substitute the values we get}\\ \\ tan \theta=\frac{-5/7}{\frac{\sqrt{24}}{7}}\\ \\ tan \theta=\frac{-5}{\sqrt{24}}\\  [/tex]Hence the correct option is C.